Methods for determination of parameters for a procedure, for estimation of cardiopulmonary function and for fluid delivery

ABSTRACT

Methods of determining at least one parameter for an injection procedure to be performed in combination with an imaging procedure may include injecting a test bolus of a contrast enhancement fluid having a contrast enhancing agent, scanning regions of interest with an imaging system as the test bolus flows therethrough to obtain therefrom a contrast time enhancement curve for each region of interest, extracting at least one discrete data point from each of the contrast time enhancement curves such that each of the discrete data points constitutes a pair of measurements on the contrast time enhancement curve corresponding thereto, substituting into a model the discrete data points extracted from the contrast time enhancement curves to obtain an estimate of values of physiological variables, and using the estimate to determine via the model the at least one parameter for the injection procedure to be performed in combination with the imaging procedure.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a national stage application of PCT/US2008/67982,filed Jun. 24, 2008, which claims the benefit of U.S. Provisional PatentApplication Ser. No. 60/950,148, filed Jul. 17, 2007, the disclosure ofwhich is incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention is related to devices, systems and methods fordetermination of parameters for a procedure, for estimation ofcardiopulmonary function and for fluid delivery, and, particularly, todevices, systems and methods for delivery of a pharmaceutical fluid to apatient based upon estimation of cardiovascular function (for example,cardiac output) of the patient, and, especially for delivery of acontrast medium to a patient during a medical injection procedure.

The following information is provided to assist the reader to understandthe invention disclosed below and the environment in which it willtypically be used. The terms used herein are not intended to be limitedto any particular narrow interpretation unless clearly stated otherwisein this document. References set forth herein may facilitateunderstanding of the present invention or the background of the presentinvention. The disclosure of all references cited herein areincorporated by reference.

The administration of contrast medium (with, for example, a poweredinjector) for radiological exams typically starts with the clinicianfilling an empty, disposable syringe with a certain volume of contrastagent pharmaceutical. In other procedures, a syringe pre-filled withcontrast agent is used. The clinician then determines a volumetricflow-rate and a volume of contrast to be administered to the patient toenable a diagnostic image. An injection of saline solution, having avolume and flow rate determined by the operator, often follows theadministration of contrast agent into the veins or arteries. A number ofcurrently available injectors allow for the operator to program aplurality of discrete phases of volumetric flow rates and volumes todeliver. For example, the SPECTRIS SOLARIS® and STELLANT® injectorsavailable from Medrad, Inc. of Indianola, Pa., provide for entry of upto and including six discrete pairs or phases of volumetric flow rateand volume for delivery to a patient (for example, for contrast and/orsaline). Such injectors and injector control protocols for use therewithare disclosed, for example, in U.S. Pat. No. 6,643,537 and PublishedU.S. Patent Application Publication No. 2004-0064041, the disclosures ofwhich are incorporated herein by reference. The values or parameterswithin the fields for such phases are generally entered manually by theoperator for each type of procedure and for each patient undergoing aninjection/imaging procedure. Alternatively, earlier manually enteredvalues of volume and flow rate can be stored and later recalled from thecomputer memory. However, the manner in which such parameters are to bedetermined for a specific procedure for a specific patient continues toundergo development.

In that regard, differences in contrast dosing requirements fordifferent patients during imaging and other procedures have beenrecognized. For example, U.S. Pat. No. 5,840,026, the disclosure ofwhich is incorporated herein by reference, discloses devices and methodsto customize the injection to the patient using patient specific dataderived before or during an injection. Although differences in dosingrequirements for medical imaging procedures based upon patientdifferences have been recognized, conventional medical imagingprocedures continue to use pre-set doses or standard delivery protocolsfor injecting contrast media during medical imaging procedures. Giventhe increased scan speed of recently available CT scanners includingMDCT (or MSCT) scanners, single phase injections are dominant overbiphasic or other multiphasic injections in regions of the world wheresuch fast scanners are used. Although using standard, fixed orpredetermined protocols (whether uniphasic, biphasic or multiphasic) fordelivery simplifies the procedure, providing the same amount of contrastmedia to different patients under the same protocol can produce verydifferent results in image contrast and quality. Furthermore, with theintroduction of the newest MDCT scanners, an open question in clinicalpractice and in the CT literature is whether the standard contrastprotocols used with single-slice, helical scanners will translate wellto procedures using the MDCT machines.

A few studies have attempted quantitative analyses of the injectionprocess during CT angiography (CTA) to improve and predict arterialenhancement. For example, Bae and coworkers developed pharmacokinetic(PK) models of the contrast behavior and solved the coupled differentialequation system with the aim of finding a driving function that causesthe most uniform arterial enhancement. K. T. Bae, J. P. Heiken, and J.A. Brink, “Aortic and hepatic contrast medium enhancement at CT. Part I.Prediction with a computer model,” Radiology, vol. 207, pp. 647-55(1998); K. T. Bae, “Peak contrast enhancement in CT and MR angiography:when does it occur and why? Pharmacokinetic study in a porcine model,”Radiology, vol. 227, pp. 809-16 (2003); K. T. Bae et al., “MultiphasicInjection Method for Uniform Prolonged Vascular Enhancement at CTAngiography: Pharmacokinetic Analysis and Experimental Porcine Method,”Radiology, vol. 216, pp. 872-880 (2000); U.S. Pat. Nos. 5,583,902,5,687,208, 6,055,985, 6,470,889 and 6,635,030, the disclosures of whichare incorporated herein by reference. An inverse solution to a set ofdifferential equations of a simplified compartmental model set forth byBae et al. indicates that an exponentially decreasing flow rate ofcontrast medium may result in optimal/constant enhancement in a CTimaging procedure. However, the injection profiles computed by inversesolution of the PK model are profiles not readily realizable by most CTpower injectors without major modification.

In another approach, Fleischmann and coworkers treated thecardiovascular physiology and contrast kinetics as a “black box” anddetermined its impulse response by forcing the system with a short bolusof contrast (approximating a unit impulse). In that method, one performsa Fourier transform on the impulse response and manipulates thistransfer function estimate to determine an estimate of a more optimalinjection trajectory than practiced previously. D. Fleischmann and K.Hittmair, “Mathematical analysis of arterial enhancement andoptimization of bolus geometry for CT angiography using the discreteFourier transform,” J Comput Assist Tomogr, vol. 23, pp. 474-84 (1999),the disclosure of which is incorporated herein by reference.

Uniphasic administration of contrast agent (typically, 100 to 150 mL ofcontrast at one flow rate) results in a non-uniform enhancement curve.See, for example, D. Fleischmann and K. Hittmair, supra; and K. T. Bae,“Peak contrast enhancement in CT and MR angiography: when does it occurand why? Pharmacokinetic study in a porcine model,” Radiology, vol. 227,pp. 809-16 (2003), the disclosures of which are incorporated herein byreference. Fleischmann and Hittmair thus presented a scheme thatattempted to adapt the administration of contrast agent into a biphasicinjection tailored to the individual patient with the intent ofoptimizing imaging of the aorta. A fundamental difficulty withcontrolling the presentation of CT contrast agent is that hyperosmolardrug diffuses quickly from the central blood compartment. Additionally,the contrast is mixed with and diluted by blood that does not containcontrast.

Fleischmann proscribed that a small bolus injection, a test bolusinjection, of contrast agent (16 ml of contrast at 4 ml/s) be injectedprior to the diagnostic scan. A dynamic enhancement scan was made acrossa vessel of interest. The resulting processed scan data (test scan) wasinterpreted as the impulse response of the patient/contrast mediumsystem. Fleischmann derived the Fourier transform of the patienttransfer function by dividing the Fourier transform of the test scan bythe Fourier transform of the test injection. Assuming the system was alinear time invariant (LTI) system and that the desired output timedomain signal was known (a flat diagnostic scan at a predefinedenhancement level) Fleischmann derived an input time signal by dividingthe frequency domain representations of the desired output by that ofthe patient transfer function. Because the method of Fleischmann et. al.computes input signals that are not realizable in reality as a result ofinjection system limitations (for example, flow rate limitations), onemust truncate and approximate the computed continuous time signal.

In addition to problems of control with current injector systems, manysuch systems lack convenience and flexibility in the manner in which theinjector systems is operated. In that regard, the complexity of medicalinjection procedures and the hectic pace in all facets of the healthcare industry place a premium on the time and skills of an operator.

In many current quantitative analysis techniques, clinicalpracticalities thus diminish the chances of adoption into regular use.Physiological models can require the estimation of many physiologicparameters a priori (for example, cardiac output, organ and great vesselblood volumes, permeability factors). The models may not be welloriented towards per-patient adaptation based on test-bolus enhancementbecause of certain mathematical limitations. Moreover, methodologies inwhich an impulse response is determined using a short bolus of contrastcan be difficult to implement practically because satisfactory means donot exist to easily transfer time-bolus enhancement data between ascanner and an injection system.

Although advances have been made in the control of fluid deliverysystems to, for example, provide a desirable time enhancement curve andto provide for patient safety, it remains desirable to develop improveddevices, systems, and method for delivery of fluids to a patient.

SUMMARY OF THE INVENTION

In one aspect, the present invention provides a method of determining atleast one parameter for an imaging procedure including the injection ofa contrast enhancement fluid which includes a contrast enhancing agent.The method includes substituting into a model discrete point datadetermined from at least one contrast time enhancement curve measuredusing an imaging system for a first region of interest resulting frominjection of a bolus of the contrast enhancement fluid. In severalembodiments, a sufficient number of data points can be substituted intothe model to determine values for physiological variables in the model.The variables can, for example, be related to cardiopulmonary function.

In a number of embodiments, at least one data point from at least asecond contrast time enhancement curve for a second region of interestmeasured using the imaging system is substituted into the model.

The at least one parameter can, for example, be a parameter of at leastone phase of an injection procedure for the injection of the contrastenhancement fluid or a parameter of the imaging system.

In several embodiments, data from the time enhancement curve of thefirst region of interest corresponds to a first pass of contrastenhancement fluid through the first region of interest, and data fromthe time enhancement curve of the second region of interest correspondsto a first pass of contrast enhancement fluid through the second regionof interest.

An analyzed portion of the time enhancement curve of the first region ofinterest can, for example, overlap an analyzed portion of the timeenhancement curve of the second region of interest in time. At least onecontrast enhancing agent concentration on one of the contrastenhancement curves at a certain time can be related to a contrastenhancing agent concentration on the other of the contrast enhancementcurves at the certain time or a time in proximity to the certain timeusing a conservation of mass balance. In several embodiments, it isassumed that the loss of contrast enhancement fluid between the firstregion of interest and the second region of interest is negligible. Inseveral embodiments, it is assumed that the blood volume for the firstregion of interest is equal to the blood volume for the second region ofinterest.

The model can be a physiological model in which cardiac output and bloodvolume are variables. Cardiac output and blood volume between theinjection site and the measurement point can be calculated for apatient. Subsequently, parameters for a procedure protocol (for example,an imaging procedure) can determined using the physiological model oranother model (which can, for example, be a parametric or anonparametric model). For example, an optimization procedure can beperformed to determine one or more parameters.

In several embodiments, a time to peak enhancement for first region ofinterest enhancement T₁ and a time to peak enhancement for the secondregion of interest enhancement T₂ are input. Concentration at peakenhancement for the first region of interest enhancement C₁(T₁) andconcentration at peak enhancement for the second region of interestenhancement C₂(T₂) are also input.

The distribution of contrast material injected into each region ofinterest from a peripheral injection site can, for example, be describedby the following analytical solution of a physiological model:

${C_{o}(t)} = \{ {\begin{matrix}{\frac{Q_{inj}}{Q_{CO}}{C_{i}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}t}} )}} \\{{C_{o}( T_{inj} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({t - T_{inj}})}}}\end{matrix}\begin{matrix}{t \leq T_{inj}} \\{t > T_{inj}}\end{matrix}} $wherein the origin, t=0, corresponds to the time at which contrastarrives in the region of interest, Q_(inj) [ml/s] is the injection flowrate, T_(inj) [s] is the injection duration, Q_(CO) is the cardiacoutput [ml/s], V_(B) is the blood volume between the injection site andmeasurement point [ml], C_(i) is the concentration of contrast in acontrast source from which contrast is injected into the patient, andC_(o)(t) is the blood concentration in the region of interest of theagent at time t.

Concentration can, for example, be related to enhancement level by theformula:C _(O)(t)=s(t)/Kwherein s(t) [Hounsfield units or HU] is enhancement level at time t andK [mgI/ml] is a conversion factor.

T_(inj) can, for example, be the amount of time between arrival ofcontrast enhancement agent and the time to peak enhancement.

Blood concentration at T_(inj) can be provided by:

${C_{o}( T_{inj} )} = {\frac{\max\;{s_{2}( T_{2} )}}{K} = {C_{2}( T_{2} )}}$wherein max s₂(T₂) [Hu] is the maximum enhancement level in the secondregion of interest and C₂(T₂) is the concentration at peak enhancementfor the second region of interest enhancement.

Contrast enhancing agent concentration on the first contrast enhancementcurve at time T₂ can be related to a contrast enhancing agentconcentration on the second contrast enhancement curves at time T₂ usingthe following equationC ₁(T ₂)≈C ₁(T ₁)−C ₂(T ₂).

Blood volume V_(B) can be determined using one of the followingformulas:

$V_{B} = {{\frac{{- T_{1}}Q_{CO}}{\log\lbrack {1 - {\frac{C_{1}( T_{1} )}{Q_{inj}C_{i}}Q_{CO}}} \rbrack}\mspace{14mu} V_{B}} = {\frac{{- ( {T_{2} - T_{1}} )}Q_{CO}}{\log\lbrack \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} \rbrack}.}}$

Cardiac output Q_(CO) can be determined using the following formula:

$Q_{CO} = {\frac{Q_{inj}}{C( T_{1} )}{{C_{i}\lbrack {1 - ( \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} )} \rbrack}^{\frac{T_{1}}{T_{2} - T_{1}}}.}}$Q_(CO) can be used in the model in which Q_(CO) is a variable todetermine the at least one parameter.

The concentration of contrast agent at peak enhancement C(T_(Peak))(sometimes written herein simply as C_(Peak)) at the time of peakenhancement T_(Peak) in the second region of interest of an imaginginjection can be related to the injection flow rate Q_(inj) of theimaging injection and the injection duration T_(inj) of the imaginginjection using the formula:

${C( T_{Peak} )} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}$

A concentration of contrast agent in the second region of interest attime of a scan start, C(T_(start)) (sometimes written herein simply asC_(start)), can be provided by:

${C( T_{Start} )} = \frac{\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}{1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}} + {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T_{inj} - {\Delta\; T}})}}}$wherein ΔT is the scan duration and wherein C(T_(start)) is equal toC(T_(start)+ΔT).

C(T_(Peak)) and C(T_(start)) enhancements can, for example, bedetermined for admissible input values for T_(inj) and Q_(inj) wherein amaximum Q_(inj) and a minimum Q_(inj) and a maximum T_(inj) and aminimum T_(inj) can be established. Maximum T_(inj) can, for example, beestablished as a function of scan duration plus a constant, and minimumT_(inj) can, for example, be established as the scan duration.

The values for the diagnostic protocol flow rate Q*_(inj) and injectionduration T*_(inj) can, for example, be determined which are thearguments that minimize the cost function:

$Q_{inj}^{, \star},{T_{inj}^{\star} = {\underset{Q_{inj},T_{inj}}{\arg\;\min}{( {{{{DesiredPeak} - {C( T_{Peak} )}}} + {{{DesiredTarget} - {C( T_{start} )}}}} ).}}}$

In another embodiment, wherein the first region of interest is a regionof interest indicative or concentration/enhancement in the right heart(for example, the pulmonary artery) and the second region of interest isa region of interest indicative or concentration/enhancement in the leftheart (for example, the ascending aorta), values for the diagnosticprotocol flow rate can be determined which are the arguments thatminimize the cost function:

$T_{start}^{\star},Q_{inj}^{\star},R_{1}^{\star},{\Delta\; T_{{inj}\; 1}^{\star}},R_{2}^{\star},{{\Delta\; T_{inj2}^{\star}} = {\underset{\underset{\underset{R_{2},{\Delta\; T_{{inj}\; 2}}}{R_{1},{\Delta\; T_{{{inj}\; 1},}}}}{T_{start},Q_{inj},}}{\arg\;\min}\begin{pmatrix}{{{C_{{LH} - {Peak}} - C_{{LH} - {Peak} - {Desired}}}} +} \\{{{C_{{LH} - {Start}} - C_{{LH} - {Target} - {Desired}}}} +} \\{{{C_{{LH} - {End}} - C_{{LH} - {Target} - {Desired}}}} +} \\{{\alpha{{C_{{RH} - {Start}} - C_{{RH} - {Target} - {Desired}}}}} +} \\{{\alpha{{C_{{RH} - {End}} - C_{{RH} - {Target} - {Desired}}}}} +} \\{{\beta{{Q_{inj} - Q_{TB}}}} +} \\{\gamma,{{if}( {{Q_{inj}( {{R_{1}\Delta\; T_{{inj}\; 1}} + {R_{2}\Delta\; T_{{inj}\; 2}}} )} > V_{Load}} )}}\end{pmatrix}}}$wherein T_(start) is a time of start of a scan, R₁ is a rate ofinjection in a phase wherein only contrast medium is injected, ΔT_(inj1)is the time of duration of the phase wherein only contrast medium isinjected, R₂ is a rate of injection in a phase wherein contrast mediumand diluent are injected, ΔT_(inj2) is the time of duration of the phasewherein contrast medium and diluent are injected, C_(LH-Peak) is acalculated concentration at peak enhancement in the left heart,C_(LH-Desired) is a desired concentration at peak enhancement in theleft heart, C_(LH-Start) is a calculated concentration in the left heartat the time of start of the scan, C_(LH-Target-Desired) is a desiredconcentration in the left heart at the time of start of the scan,C_(LH-End) is a calculated concentration in the left heart at the timeof the end of the scan or T_(End), C_(RH-Start) is a calculatedconcentration in the right heart at the time of start of the scan,C_(RH-Target-Desired) is a desired concentration in the right heart atthe time of start of the scan, and C_(RH-End) is a calculatedconcentration in the right heart at the time of the end of the scan, αis a weighting factor, β is a weighting factor and γ is a penalty. γcan, for example, be a defined value if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) is true (for example, 1000)and can be 0 if (Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) is not true,wherein V_(Load) is the total volume of contrast available.

C_(LH-Peak) can, for example, be the greater of the value calculated asfollows:

$\mspace{79mu}{C_{{LH} - {Peak}} = {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}\; 1}}} )}\mspace{20mu}{or}}}\mspace{14mu}$$C_{{LH} - {Peak}} = {{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}\; 1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}\; 2}}} + {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}\; 2}}} )}}}$

The concentration C_(T) in the right heart or the left heart asapplicable at a time T, which is either T_(start) or T_(end), whenT<(T_(arr)+ΔT_(inj1)), wherein T_(arr) is either the time of arrival ofcontrast at the right heart or at the left heart as applicable, can becalculated by the following formula:

$C_{T} = {\frac{Q_{inj}}{Q_{CO}}C_{i}{{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - T_{\;{arr}}})}}} )}.}}$

The concentration C_(T) in the right heart or the left heart asapplicable at a time T, when,(T_(arr)+ΔT_(inj1))<T<(T_(arr)+ΔT_(inj1)+ΔT_(inj2)) can be calculated bythe following formula:

$C_{T} = {{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}\; 1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{\;{arr}} + {\Delta\; T_{{inj}\; 1}}})}})}}} + {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{\;{arr}} + {\Delta\; T_{{inj}\; 1}}})}})}}} )}}}$

The concentration C_(T) in the right heart or the left heart asapplicable at a time T, when T>(T_(arr)+ΔT_(injA)+ΔT_(injAB)), can becalculated by the following formula:

$C_{T} = \begin{pmatrix}{{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}2}}} +} \\{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}2}}} )}}\end{pmatrix}$${\mathbb{e}}^{{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{arr} + {\Delta T}_{{inj}1} + {\Delta T}_{{inj}2}})}})}}\;}$

In another aspect, the present invention provides a parameter generationsystem to determine at least one parameter for a procedure includinginjection of a contrast enhancement fluid which includes a contrastenhancing agent adapted to enhance contrast in an imaging system. Thesystem includes an input system to receive point data from at least afirst time enhancement curve from a first region of interest resultingfrom injection of a test bolus and at least one processor incommunicative connection with the input system to determine the at leastone parameter based at least in part upon substitution of the point datainto a model. As described above, a sufficient number of data points canbe substituted into the model to determine values for physiologicalvariables in the model. The variables can, for example, be related tocardiopulmonary function.

At least one data point from at least a second contrast time enhancementcurve measured using the imaging system in at least a second region ofinterest can also be input into the input system and substituted intothe model.

The at least one parameter can, for example, be a parameter of at leastone phase of an injection procedure for the injection of the contrastenhancement fluid or a parameter of the imaging system.

Data from the time enhancement curve of the first region of interest cancorrespond to a first pass of contrast enhancement fluid through thefirst region of interest, and data from the time enhancement curve ofthe second region of interest can correspond to a first pass of contrastenhancement fluid through the second region of interest.

An analyzed portion of the time enhancement curve of the first region ofinterest can, for example, overlap an analyzed portion of the timeenhancement curve of the second region of interest in time. At least onecontrast enhancing agent concentration on one of the contrastenhancement curves at a certain time can be related to a contrastenhancing agent concentration on the other of the contrast enhancementcurve at the certain time or a time in proximity to the certain timeusing a conservation of mass balance.

In several embodiments, it is assumed that the loss of contrastenhancement fluid between the first region of interest and the secondregion of interest is negligible.

In another aspect, the present invention provides an injector systemincluding a parameter generation system to determine at least oneparameter for a procedure including injection of a contrast enhancementfluid which includes a contrast enhancing agent adapted to enhancecontrast in an imaging system. The parameter generation system includesan input system to input/receive (either manually or in an automated,electronically communicated manner) point data from at least a firsttime enhancement curve from a first region of interest resulting frominjection of a test bolus and at least one processor in communicativeconnection with the input system to determine the at least one parameterbased at least in part upon substitution of the point data into a model.

In a further aspect, the present invention provides a system includingan injector system, an imaging system and parameter generation system todetermine at least one parameter for a procedure including injection ofa contrast enhancement fluid which includes a contrast enhancing agentadapted to enhance contrast in an imaging system. The parametergeneration system includes an input system to input/receive point datafrom at least a first time enhancement curve from a first region ofinterest resulting from injection of a test bolus and at least oneprocessor in communicative connection with the input system to determinethe at least one parameter based at least in part upon substitution ofthe point data into a model.

In still a further aspect, the present invention provides a method ofdetermining at least one parameter for a procedure, including:substituting into a model discrete point data determined from at leastone time concentration curve measured using a sensor for at least afirst region of interest resulting from injection of a bolus of the apharmaceutical. A sufficient number of data points can be substitutedinto the model to determine values for physiological variables in themodel. The variables can, for example, be related to cardiopulmonaryfunction. At least one data point from at least a second contrast timeenhancement curve for a second region of interest can be measured andsubstituted into the model.

As used herein with respect to an injection procedure, the term“protocol” refers generally to a group of parameters for a procedure(for example, an imaging procedure involving the injection of a contrastenhancement fluid or contrast medium) Injection parameter can, forexample, include as flow rate, volume injected, injection duration,contrast agent concentration etc. that define, for example, the timingof, amount of, and/or the nature of fluid(s) to be delivered to apatient during an injection procedure. Such parameters can change overthe course of the injection procedure. As used herein, the term “phase”refers generally to a group of parameters that define, for example, thetiming of, amount of, and/or the nature of fluid(s) to be delivered to apatient during a period of time (or phase duration) that can be lessthan the total duration of the injection procedure. Thus, the parametersof a phase provide a description of the injection over a time instancecorresponding to the time duration of the phase. An injection protocolfor a particular injection procedure can, for example, be described asuniphasic (a single phase), biphasic (two phases) or multiphasic (two ormore phases, but typically more than two phases). Multiphasic injectionsalso include injections in which the parameters can change continuouslyover at least a portion of the injection procedure.

Scanner parameters that can be determined include, but are not limitedto, the amount of radiation transmitted to the patient, power inputs(for example, voltage or current), timing (for example, scan start time,stop time, delay time and/or duration).

The present invention, along with the attributes and attendantadvantages thereof, will best be appreciated and understood in view ofthe following detailed description taken in conjunction with theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic representation of a Fick Principles modelused in several embodiment of fluid delivery systems and methods of thepresent invention.

FIG. 2A illustrates a simplified model of contrast injection.

FIG. 2B illustrates an injection system and imaging system of thepresent invention and a graphical user interface for use in connectionwith the injection system setting forth areas for parameters forinjection flow rate, injection volume and injection duration for, forexample, three phase of injection fluids A and B.

FIG. 3 illustrates sample concentration curves for a timing or testbolus, wherein times to peak and peak enhancements are labeled, and theconcentration at a second point (C_(PA)(T₂)) on the pulmonary artery(PA) curve is approximated by the difference in peaks.

FIG. 4 is a sample concentration curves for a diagnostic injection,showing the peak and target concentrations in the scan window, wherein ascan start time T_(start) and an injection duration T_(inj) are relativeto the arrival time of the contrast in the left heart.

FIG. 5 illustrates a contour plot of the solution space for Equation (8)wherein C_(i)=370 mgI/ml, C_(Peak)=350 HU, C_(Target)=300 HU, Q_(CO)=6.1L/min, and V_(B)=0.72 L.

FIG. 6 illustrates a surface plot of the solution space for Equation (8)wherein C_(i)=370 mgI/ml, C_(Peak)=350 HU, C_(Target)=300 HU, Q_(CO)=6.1L/min, and V_(B)=0.72 L.

FIG. 7A illustrates an injection truncation scenario when the computedinjection extends beyond the end of the scan.

FIG. 7B illustrates the truncated protocol resulting from the truncationscenario of FIG. 7A.

FIG. 8A illustrates a protocol truncation scenario in which the computedinjection duration terminates without enough time for the final volumeof contrast to arrive in the territory of interest before the scan ends.

FIG. 8B illustrates the “fixed” protocol resulting from the protocoltruncation scenario of FIG. 8A.

FIG. 9A illustrates one embodiment of a manner in which a dual-flow(dilution) phase is computed, wherein an objective is to have dilutedcontrast arriving in the territory of interest as the scan starts; andwherein undiluted contrast will be flooding the right heart as the scanstarts.

FIG. 9B illustrates the protocol generated using the dual-flowcomputation of FIG. 9A.

FIG. 10A illustrates a comparison over 15 sample subjects of flow ratesdetermined using a methodology (A) set forth in PCT International PatentApplication No. PCT/US2007/026194 and a first embodiment of amethodology (B) of the present invention.

FIG. 10B illustrates data obtained in a study group of 70 patientsscheduled for clinically indicated dual source CT or DSCT studies underone embodiment of the present invention

FIG. 10C illustrates mean attenuation (HU) for each of the anatomyregions studied for the study group of FIG. 10B.

FIG. 10D illustrates mean contrast medium volume used in the studies ofeach of the study group and a control group.

FIG. 10E illustrates a graph of contrast medium savings (mL) as afunction of cardiac output.

FIG. 10F illustrated mean attenuation for each of the control group andthe study group for each of the anatomical regions studied.

FIG. 11 illustrates an example of relative timing and diagnosticinjection protocol phases, scan and enhancement curves.

FIG. 12 illustrates a comparison of iodine administration rate over 15sample subjects as determined using the methodology (A) as set forth inPCT International Patent Application No. PCT/US2007/026194, using afirst embodiment of a methodology (B) of the present invention in whicha dilution ratio for a dilution phase is fixed and right heartenhancement factors/arguments are not included in an optimization costfunction, and using a second embodiment of a methodology (C) of thepresent invention in which a dilution ratio for a dilution phase variesand right heart enhancement factors/arguments are included in anoptimization cost function.

FIG. 13 illustrates a comparison of contrast medium volume (CM volume)rate over 15 sample subjects as determined using the methodology (A) asset forth in PCT International Patent Application No. PCT/US2007/026194,using a first embodiment of a methodology (B) of the present inventionin which a dilution ratio for a dilution phase is fixed and right heartenhancement factors/arguments are not included in an optimization costfunction, and using a second embodiment of a methodology (C) of thepresent invention in which a dilution ratio for a dilution phase variesand right heart enhancement factors/arguments are included in anoptimization cost function.

FIG. 14 illustrates clinical data collected from ten subjects undergoingDSCT cardiac imaging (Siemens Definition) under a second embodiment ofthe present invention.

DETAILED DESCRIPTION OF THE INVENTION

In the present invention, variables in a model that is predictive oftemporal changes in concentration in a region or regions of interestwithin a patient are determined or estimated using data from at leastone concentration profile for a pharmaceutical (that is, concentrationas a function of time) in at least one region of interest. Dependingupon the number of variables present within the model, a number ofdiscrete data points are taken from one or more contrast concentrationprofiles (that are, for example, provided by time enhancement curvesgenerated using an imaging system) to provide an estimation of thevalues of such variables. In a number of models, such variables arerelated to cardiopulmonary function (that is, cardiac, pulmonary andvascular function/dynamics). For example, in a representative embodimentof a model used in the present invention, two variables, cardiac output(Q_(CO)) and blood volume (V_(B)), are unknown. Two discrete data points(that is, two concentrations at two times) are used to determineestimates of those variable.

In the case of imaging systems or scanners currently in use, it can bedifficult (for example, as a result of noise in the signal or otherdifficulty in reading/determining data points from the imaging system)to accurately determine multiple data points upon one or more timeenhancement curves. However, in a number of models, it is relativelystraightforward to determine, for example, a peak enhancement and anassociated time to peak enhancement. Indeed, software associated withsuch systems is often optimized to determine peak enhancement and timeto peak enhancement.

In several embodiments of the present invention, an estimation of modelvariables (for example, variables related to cardiopulmonary function)is made upon analysis of at least two concentration profiles of apharmaceutical as a function of time and using point data from suchconcentration profiles to determine variables as described above. In anumber of such embodiments, concentration profiles at more than oneregion of interest are related and the concentrations and timesassociated with the peak concentrations are used to determine variablesin a model as described above. For example, in the case of a modelincluding two physiological variables, peak enhancements/concentrationsand times to peak enhancement for a first region of interest (that is,location within the body of a patient) and for at least a second regionof interest can be used to determine the variables.

One skilled in the art appreciates that the analysis can be performed inassociation with generally any type of pharmaceutical in connection withan appropriate sensor system to measure concentration profiles of thepharmaceutical at two or more locations or regions of interest withinthe body. The combination of injection of a contrast enhancing fluid andthe use of an imaging system to measure enhancement/concentration at aplurality of regions of interest provides an effective and minimallyinvasive technique for estimation of, for example, cardiovascularfunction in the present invention, and the combination or contrastinjection/CT image scanning is discussed as a representative exampleherein. Once an estimation of cardiovascular parameters (for example,cardiac output, blood volume etc.) is made those parameters can be usedin determining parameters for any number of procedures including, forexample, parameters for therapeutic drug delivery, parameters for animaging procedure etc.

In the case of injection of a contrast enhancement fluid, a suitableanalysis of a full test-bolus time enhancement curve (sometimes referredto herein simply an enhancement curve) may enable the full estimation ofcardiopulmonary and vascular parameters necessary for developing optimalcontrast injections. However, such methodologies are limited, forexample, because satisfactory means do not exist to easily transfertime-bolus enhancement data between a scanner and an injection system.Although sharing of a complete time-enhancement curve between a scannerand an injection system for analysis therein is not currentlyimplemented in available scanners and injectors, intermediatealgorithmic options can still incorporate data accessible fromtime-bolus enhancement curves. Such data can, for example, provide thebest available indication of a patient's cardiovascular dynamics. In thesystems and method of PCT International Patent Application No.PCT/US2007/026194, the disclosure of which is incorporated herein byreference, iodine administration rate of contrast agent/material isadjusted based on the patient's weight and a scan duration. See alsoPublished PCT Application Nos. WO/2006/058280 and WO/2006/055813, thedisclosures of which are incorporated herein by reference. Furtherrefinement of the determined diagnostic injection protocol is made basedon the peak enhancement value and time to peak of a test bolusenhancement curve in the patient's ascending aorta/aortic arch. Thatdata from the time-enhancement curve are used in protocol generation todetermine the scan delay, to determine the dilution ratio and thusIodine administration rate of a second, dual-flow phase (in whichcontrast media and a diluent are simultaneously injected), and todetermine at what point the injection system should stop injecting toprevent excess injection (for that patient) of contrast material. Thatmethodology has shown promise in reducing the dependency of contrastenhancement on patient habitus, better consistency of right ventricleenhancement, and easing technologist workflow during the execution ofpersonalized injection protocols. That methodology can be furtheroptimized if one relaxes the constraint of eliminating contrast residualand allows for the manipulation of flow rates after the test bolus hasbeen administered.

It is well known that cardiac output and vascular blood volume areimportant parameters affecting contrast bolus propagation. If the entiretime enhancement curve from a test bolus is available, robust andreliable estimates of these parameters can be made in a parametric ornon-parametric paradigm. Requiring a technologist to manually enter allor even more than 4 points from a time enhancement curve can be overlytaxing. However, there is insufficient useful information from the peakconcentration and time to peak of only a single test bolus curve to makea quantitative estimate of cardiac output (beyond stating that aninverse relationship exists between the peak enhancement and cardiacoutput).

Use of regression formulae with weight, scan duration, concentration andtest bolus enhancement data to calculate cardiac output and vascularblood volume is also less than optimal. For example, the regressioncoefficients generated from one set of data are not necessarily validfor predicting a treatment response of another group. A simple nomogramcan also be generated, the heuristics of which map test bolusenhancement data to injection flow rate. Another approach is to estimatethe total blood volume from look-up table relationships and divide by afactor to consider only the volume between the injection point and, forexample, the cardiac anatomy. These classes of algorithms are less thanoptimal, however, because they are not predicated on physicalprinciples, are not robust to variations in parameter and measurementuncertainty, and are difficult to validate. Furthermore, thosealgorithms do not provide for easy manipulation of other injectionparameters such as dilution ratio of contrast/saline, scan delay, andinjection duration of contrast material.

As described above, in several embodiments, the systems and methods ofthe present invention provide data-driven, parametric estimationtechniques that use, for example, the times to peak and peakconcentrations/enhancements of at least two timeconcentration/enhancement curves (each for a different region ofinterest or ROI) generated, for example, from a test or timing bolus (orinjection) to estimate the subject's cardiac output and blood volumebetween, for example, the injection site and cardiac anatomy. As clearto one skilled in the art, more than two ROIs can be use in theestimation techniques of the present invention.

The estimations of physiological variables (for example, cardiac outputand/or blood volume) are used in a model such as a pharmacokinetic modelto determine suitable injection parameters to, for example, achieve adesired enhancement in a region of interest. The same model via whichthe physiological parameters were determined can, for example, be usedto determine protocol parameters (for example, injection parametersand/or imaging/scanning parameters). Alternatively or additionally, thevariables can be used in connection with at least one other model (whichcan, for example, be a parametric model or a nonparametric model) todetermine protocol parameters. Various models are, for example,discussed in PCT International Patent Application No. PCT/US2007/026194and in Published PCT Application Nos. WO/2006/058280 and WO/2006/055813.In a number of embodiments, for example, an optimized protocolgeneration algorithm, computes a flow rate, an injection duration and/orother parameters to achieve predetermined enhancement levels throughoutthe scan duration using the determined physiological variables (forexample, estimated cardiac output and blood volume) as input.

In several embodiments, the first ROI (during the timing bolusprocedure) occurs first in the circulation of the injected contrastenhancing fluid (that is, it is closest in the circulation path to theinjection site) and the second ROI is the ROI of primary interest in theimaging procedure. However, injection parameters can be determined toeffect a desired enhancement in either or both the first and second ROIs(or one or more other ROIs). In general, the ROIs used in the parametricestimation techniques can be relatively close to each other in the bloodcirculation path such that the first pass enhancement curves overlapeach other over at least a portion of the enhancement curves. Thetechniques of the present invention are, for example, well suited forROIs that are within blood vessels such as in the case of angiographystudies. However, the techniques of the present invention are alsosuitable for use in connection with tissue (such as studies of tumoruptake).

In several representative studies of the present invention, a first timeenhancement curve was generated with an ROI in, for example, thepulmonary trunk and a second time enhancement curve was generated froman ROI in the ascending aorta. The data were, for example, generatedfrom serial computed tomography or CT scanning at the level of thepulmonary trunk starting, for example, 4-5 seconds after the start ofcontrast injection. One skilled in the art appreciates that the systemsand methods of the present invention are applicable in imagingtechniques other than CT, including, but not limited to, magneticresonance imaging (MRI) scans, Positron Emission Tomography (PET) scansand Single Photon Emission Computed Tomography (SPECT) scans. Likewise,one skilled in the art appreciates, that many different regions ofinterest can be used as the first and second regions of interest. Forexample, a first ROI and second ROI can be the femoral artery and thepopliteal vein in the legs for the performance of peripheralangiography. In the case of neuro-CT Angiography, any of the basilararteries and corresponding draining veins can be used as ROIs during thefirst pass of contrast material. The ROIs need not be limited to ROIsthat can be imaged, for example, in a single scan plane. The use of widevolume scanning (for example, wide volume CT scanning) can enable theuse of ROIs from various planes within the body.

In several embodiments, systems and methods of the present inventionwere based, at least in part, upon a one compartment, openpharmacokinetic (PK) model. Such a model can, for example, be suitablefor use in modeling first-pass dynamics in, for example, CT angiographyof cardiovascular structures. The input to the PK model was theconcentration of the contrast medium, flow rate and duration of theinjection. In using times to peak and peak enhancement of two timeenhancement curves to derive an estimate of the cardiac output and bloodvolume between the injection site and, for example, the aortic root, alinear relationship between measured enhancement in Hounsfield units(HU) and contrast blood concentration and conservation of mass betweenthe two parts of the cardiopulmonary circuit were assumed. Once anestimate of cardiac output was made, it can, for example, be substitutedinto the analytic solution of the PK model (and/or used in connectionwith one or more other models) to determine parameters for an imagingprocedure. In several embodiments, a minimal flow rate and injectionduration to achieve a desired peak enhancement and desired targetenhancements (defined as the HU level that should be attained at thebeginning and end of the scan) were determined.

After determining a minimal injection duration that achieves a desiredenhancement (for example, defined peak and target enhancement goals),the time at which the scan should start was deduced using the solutionof the PK model. In a number of embodiments, a constraint was theenforced that ends the injection of contrast a defined amount of time(for example, 5 seconds) before the scan is done. The actual offset fromthe end of the scan was, for example, be determined from the time topeak of the pulmonary artery time enhancement curve of the timing bolusprocedure, which was assumed to be an indicator of propagation time fromthe injection site to the right heart. Finally, a per-person dual-flow(dilution) phase was computed given the knowledge of the transit time tothe right heart. The transit time was factored into determining the timeat which dilution was “cut over”. For simplicity, a fixed ratio of 40/60(contrast/saline) was applied in several representative studies.Techniques for determining a contrast/saline ratio based upon patientspecific data which can be used in connection with the present inventionare described, for example, in PCT International Patent Application No.PCT/US2007/026194. Moreover, as discussed further below, dilution ratiocan be treated as a variable in an optimization procedure in severalembodiments of the present invention.

The following expression describes the distribution of contrast materialinjected into a central blood compartment from a peripheral injectionsite. The origin, t=0, corresponds to the time at which the contrastmaterial arrives in the region of interest (assuming plug flow of thespecies):

$\begin{matrix}{{C_{o}(t)} = \{ \begin{matrix}{\frac{Q_{inj}}{Q_{co}}{C_{i}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}t}} )}} & {t \leq T_{inj}} \\{{C_{o}( T_{inj} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({t - T_{inj}})}}} & {t > T_{inj}}\end{matrix} } & (1)\end{matrix}$

wherein Q_(inj) [ml/s] is the injection flow rate, T_(inj) [s] is theinjection duration, Q_(CO) is the cardiac output [ml/s], V_(B) is theblood volume between the injection site and measurement point [ml],C_(i) is the concentration of contrast enhancing agent (for example,iodine) in a source of contrast fluid to be delivered to the patient,and C_(o)(t) is the blood concentration of the contrast enhancing agentat time t. FIG. 1 graphically depicts this model.

As, for example, illustrated in FIG. 3, a time enhancement curves_(AO)(t) [Hounsfield units or HU] measured in a first ROI, theascending aorta (AO), results from a timing bolus injection. A timeenhancement curve s_(PA)(t) [Hounsfield units or HU] measured in asecond ROI, the pulmonary artery (PA) trunk, also results from thetiming bolus injection. In accordance with the result of previousexperimental studies, T_(inj) (the injection duration) is the time topeak enhancement as a result of the timing bolus injection. K_(HU-mgI)is the conversion factor relating HU to concentration of Iodine in vivoat the measurement location. The relationship, then, converting themeasured timing bolus enhancement curve in the ascending aorta toconcentration units [mgI/ml] is thus:

$\begin{matrix}{{C_{o}( T_{inj} )} = {\frac{\max( {s_{AO}(t)} )}{K_{HU─mgI}} \equiv C_{Peak}}} & (2)\end{matrix}$

A default value for the conversion factor K_(Hu) _(—) _(mgI) of 25 wasused. This value is within the range of 21-26 published by severalinvestigators. Variation in this constant can arise between scanners.Thus, an individual scanner generated calibration curve may be warrantedin certain situations.

Estimating Cardiac Output from Timing Bolus Point Data

As described above, in using the governing model to compute apatient-specific diagnostic protocol (including, for example, flow rateand injection duration), estimates of cardiac output (Q_(CO)) and bloodvolume between the injection site and measurement point (V_(B)) weremade. Data obtained from the timing bolus enhancement curves, where theflow rate and injection duration are known, were used to solve for thesetwo unknowns.

Ideally, an entire concentration curve would be available to determine abest fit for Q_(CO) and V_(B). At this time, however, only discrete datapoint values such as peak enhancements and times to peak in, forexample, two structures (for example, the pulmonary artery and theascending aorta) are reasonably acquired from the timing bolus data.There is, therefore, only one data point on each concentration curve,and the system is underdetermined. The acquisition of two points on asingle curve is approximated in the present invention by combining thedata points on the individual curves from each structure.

In several embodiments, a number of simplifying assumptions were made.First, it is assumed the blood volumes are the same in bothcompartments, so that the concentration is directly related to the massof iodine in the compartment. Without a relationship between the bloodvolumes in the compartments, the system is still underdetermined withtwo equations and three unknowns. Second, the system is simplified totwo single compartment models where the peak enhancements and times topeak are measured (see FIG. 2A). In this simplification, the contrast isinjected, flows into the pulmonary artery, flows into the ascendingaorta, and then flows out.

Loss of iodine in an intermediate compartment (such as the lungs) isignored. Alternatively, a simple relation can be set forth for suchloss, without introducing additional variables into the model. Given alack of enhancement data or volume information available for theintermediate compartments on a per-patient basis and the temporalresolution at which the timing bolus data are acquired, morecomprehensive models were not attempted for this computation. Thesimplified model yields C_(o)(t) curves similar to those set forth inFIG. 3.

The available measurements are C_(PA)(T₁), T₁, C_(AO)(T₂), and T₂. Att=T₁, C_(PA)(T₁)/V_(B) ml of iodine are present in the pulmonary artery.This amount of iodine is less than the amount in the test bolus becausesome has already flowed into the ascending aorta. At t=T₂,C_(AO)(T₂)/V_(B) of iodine are present in the ascending aorta, and thereis also some amount of iodine remaining in the pulmonary artery. Theshorter peak in the ascending aorta at T₂, as compared to the peak forthe pulmonary artery, is a result of the iodine left in the previouscompartment. Therefore, the second point on the C_(o)(t) curve for thepulmonary artery, C_(PA)(T₂), can be approximated by the difference inpeaks as set forth in Equation (3) below.C _(PA)(T ₂)≈C _(PA)(T ₁)−C _(AO)(T ₂)  (3)

As before, the peak of the pulmonary artery curve is defined by:

$\begin{matrix}{{C_{PA}( T_{1} )} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{1}}} )}}} & (4)\end{matrix}$

The expression for C_(2PA) on the downslope is then:

$\begin{matrix}{{{C_{PA}( T_{2} )} \approx {{C_{PA}( T_{1} )} - {C_{AO}( T_{2} )}}} = {{C_{PA}( T_{1} )}( {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T_{2} - T_{1}})}} )}} & (5)\end{matrix}$

Rearranging the latter two equations and solving for V_(B) yields:

$\begin{matrix}{\;{V_{B} = {{\frac{{- T_{1}}Q_{CO}}{\log( {1 - {\frac{C_{PA}( T_{1} )}{Q_{inj}C_{i}}Q_{CO}}} )}\mspace{20mu} V_{B}} = \frac{{- ( {T_{2} - T_{1}} )}Q_{CO}}{\log( \frac{{C_{PA}( T_{1} )} - {C_{AO}( T_{2} )}}{C_{PA}( T_{1} )} )}}}} & (6)\end{matrix}$

By equating these two expressions, one can isolate Q_(CO) as follows:

$\begin{matrix}{Q_{CO} = {\frac{Q_{inj}}{C_{PA}( T_{1} )}{C_{i}( {1 - ( \frac{{C_{PA}( T_{1} )} - {C_{AO}( T_{2} )}}{C_{PA}( T_{1} )} )^{\frac{T_{1}}{T_{2} - T_{1}}}} )}}} & (7)\end{matrix}$

This method fails if C_(PA)(T₁)<C_(AO)(T₂) (the second peak is largerthan the first peak), which should only happen when the scan is startedtoo late and the first peak is missed. Despite the simplifying modelingassumptions made, cardiac output estimates were found to be within areasonable range when both peaks are captured in the scan window.

Diagnostic Injection Protocol Generation—Methodology 1

In several embodiments of the present invention, an injection system(such as a dual syringe injector system 100 as illustrated in FIG. 2Band as, for example, disclosed in U.S. Pat. No. 6,643,537, PublishedU.S. Patent Application Publication No. 2004-0064041 and PCTInternational Patent Application No. PCT/US2007/026194) for use with thepresent invention includes two fluid delivery sources (sometimesreferred to as source “A” and source “B” herein; such as syringes) thatare operable to introduce a first fluid and/or a second fluid (forexample, contrast enhancement fluid, saline etc.) to the patientindependently (for example, simultaneously, simultaneously in differentvolumetric flow proportion to each other, or sequentially or subsequentto each other (that is, A then B, or B then A)). In the embodiment ofFIG. 2A, source A is in operative connection with a pressurizingmechanism such as a drive member 110A, and source B is in operativeconnection with a pressurizing mechanism such as a drive member 110B.The injection system includes a control system 200 in operativeconnection with injector system 100 that is operable to control theoperation of drive members 110A and 110B to control injection of fluid A(for example, contrast medium) from source A and injection of fluid B(for example, saline) from source B, respectively. Control system 200can, for example, include or be in communication with a user interfacecomprising a display 210. In the illustrated embodiment of FIG. 2B, aportion of one embodiment of a screen display is illustrated which showsareas for parameters for injection flow rate, injection volume andinjection duration for, for example, three phases of injection of fluidA and/or fluid B. The parameters for one or more such phases can bepopulated using the parameter generation systems and methods of thepresent invention. FIG. 2C illustrates another embodiment of a screendisplay for an embodiment of a system of the present invention asdiscussed below (methodology 1).

A user can be provided with the option to adjust and/or override theparameters generated (for example, via a manual input system 205including a keypad, keyboard, mouse etc. as known in the computer arts).Control system 200 can include a processor 220 (for example, a digitalmicroprocessor as known in the art) in operative connection with amemory or memory system 230.

As clear to one skilled in the art, may fluid delivery systems,including multi-patient fluid delivery systems as, for example,disclosed in U.S. Pat. Nos. 7,326,186, 7,094,216, 6,866,654, 6,972,001,6,699,219, 6,471,674, 6,306,117, 6,149,627, 6,063,052, 5,920,054,5,843,037, 5,827,219, 5,739,508 and 5,569,181 are also suitable for usein the present invention.

Imaging system 300 can, for example, be a CT system, a MagneticResonance Imager (MRI) system, an ultrasound imaging system, or aPositron Emission Tomography (PET) system) or a Single Photon EmissionComputed Tomography (SPECT) system as described above. The injectionsystem can be in communicative connection with imaging system 300.Imaging system 300 and injector system 100 can, for example, be incommunication connection via input/output ports (represented byterminations of arrows in FIG. 2B) as known in the art. In FIG. 2B,imaging system 300 and injector system 100 are, for example, illustratedto be in communicative connection via a common communication hub 400.Alternatively, a direct communication link can be established. Furtherdata from one of imaging system 300 and injection systems 100 can bemanually entered using one or more manual input systems (for example,keypads, keyboards mouse etc.) as know in the computer arts. Imagingsystem 300 and injector system or injector 100 can also be partially orfully integrated as described, for example, in Published PCTInternational Patent Application No. WO 2008/011401, the disclosure ofwhich is incorporated herein by reference. One, a plurality or all theillustrated components of the injection system and imaging system 300can also or alternatively be integrated with or incorporated withinanother, separate component that is placed in communicative connectionwith other system components.

Software embodying the systems and methods of the present invention can,for example, be embodied within one or more separate or standalonesystems represented by system 500 which can, for example, include atleast one processor (for example, a digital microprocessor), a memorysystem 520 a display 510 and a manual input system 505. In theembodiment illustrated in FIG. 2B, system 500 is shown to be incommunicative connection with communication hub 400. As described above,a direct communication link can also be established. Further data fromone or more systems can be manually entered into one or more othersystems using one or more manual input systems (for example, keypads,keyboards, a mouse etc.) as know in the computer arts. Softwareembodying the systems and methods of the present invention (including,for example, one or more executable computer algorithms therefor) can,for example, be stored in memory 530 and executed by processor 520. Asclear to one skilled in the art, all or a portion of the functionalityof the methods and/or systems of the present invention can alternativelyreside in an imaging system 300 (which can, for example, include atleast one processor 320, a memory system 330, a display 310 and a manualinput system 305) and/or in injector system 100.

For determining an appropriate flow rate and an appropriate injectionduration for a given patient in several embodiments, bloodconcentrations of contrast enhancing agent can be modeled in the sameway as in the estimation of cardiac output and blood volume. Forexample, two attributes are typically considered to be important to thegeneration of the diagnostic injection protocol: the peak concentrationand the target concentration (defined as the concentration at the startand end of the scan window) of the left heart structures. As shown inFIG. 4, the concentration at peak enhancement C_(Peak) for the leftheart/ascending aorta (the second ROI in the representative studies ofthe present invention) occurs T_(inj) seconds after the contrast arrivesin the left heart. The scan begins at T_(start), on an unknown point onthe upslope of the left heart concentration curve. It ends ΔT secondslater at T_(start)+ΔT or T_(end), where ΔT is the specified scanduration, on the downslope of the curve. To position the scan window insuch a way that enhancement is both as high and as consistent aspossible, those two values (on the upslope and downslope) can be set tobe equal and are referred to as C_(Target).

Given desired values for each of a desired peakconcentration/enhancement and a desired target concentration/enhancementin one region of interest (for example, the aorta/left heart), andequally weighting the error in peak enhancement and the error in targetenhancement in that region of interest, the following optimization canbe used (wherein “Desired” values are provided/input by, for example, anoperator):

$\begin{matrix} {{{{{{{Q_{inj}^{\star},{T_{inj}^{\star} = {{{\underset{Q_{{inj},}T_{inj}}{\arg\;\min}(  }{DesiredPeak}} - C_{Peak}}}}} +}}{DesiredTarget}} - C_{Target}}} ) & (8)\end{matrix}$

As clear to one skilled in the art, the arguments can be weighted otherthan equally in the above cost function and further arguments can beincluded. As also clear to one skilled in the art, additional oralternative optimizations can be performed.

To find Q*_(inj) and T*_(inj), the error function is defined in terms ofQ_(inj), T_(inj), and known constants, using the analytical solution tothe PK model. This is already true by definition for C(T_(Peak)) orC_(Peak):

$\begin{matrix}{C_{Peak} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} )}}} & (9)\end{matrix}$

The value of C(T_(start)) or C_(Target) on the upslope is also afunction of T_(start), the unknown time at which the scan begins.

$\begin{matrix}{C_{Target} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{start}}} )}}} & (10)\end{matrix}$

On the downslope, C_(Target) is the concentration at the end of thescan, which is a function of C_(Peak) and T_(start) (assuming the scanduration, ΔT, is fixed).

$\begin{matrix}{C_{Target} = {C_{Peak}( {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T_{start} + {\Delta T} - T_{inj}})}} )}} & (11)\end{matrix}$

Substituting in for C_(Peak) and simplifying yields:

$\begin{matrix}{C_{Target} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}( {{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T_{start} + {\Delta T} - T_{inj}})}} - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T_{start} + {\Delta T}})}}} )}}} & (12)\end{matrix}$

At this point, there are two equations (C_(Target) on the upslope andthe downslope) and two unknowns (C_(Target) and T_(start)). Aftersolving algebraically for C_(Target), the following expression in termsof only Q_(inj), T_(inj), and known constants is derived.

$\begin{matrix}{C_{Target} = \frac{\frac{Q_{inj}}{Q_{CO}}{C_{i}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} )}}{1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}} + {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T_{inj} - {\Delta T}})}}}} & (13)\end{matrix}$

Note that if T_(inj)>>ΔT, C_(Target) approaches the numerator(C_(Peak)), and if delta T>>T_(inj), C_(Target) goes to zero. Equations(9) and (13) are now substituted into equation (8) and the parametersthat minimize the cost function are determined. There are severaloptions for numerical solutions for Q*_(inj) and T*_(inj) including, butnot limited to: a “brute force” search over a reasonablerange/resolution of Q_(inj) and T_(inj); a relatively straightforwardminimization such as Nelder-Mead (simplex); or a gradient descent (thepartial derivatives can be computed analytically as well). In severalstudies, a brute force search strategy was implemented because theparameter range is well defined, the solution manifold is well behaved(as shown in the contour plot in FIG. 5 and surface plot in FIG. 6), andthe computational burden needed to search for the minimum isinsignificant, especially realizing that a computation time of severalseconds in the interval between parameter entry and protocol generationhas no impact on the procedure.

Injection Truncation and Dilution Phase Calculations

Once an initial, computed diagnostic protocol is generated (includingthe scan delay), a test is applied to ensure the contrast injection isterminated a given amount of time (for example, a few seconds) prior tothe end of the scan. One obviously does not want to inject contrastmedia after the end of the scan because that contrast will notcontribute to the diagnostic image. A more subtle consideration inoptimal protocol generation arises in that, because of the transit delayfrom the injection site to the right heart (or other ROI), contrastinjected within the time between the end of the scan and the transittime to, for example, the right heart also will not contribute to thediagnostic image. The minimum time needed for contrast to arrive in theright atrium was determined as the peak time of the pulmonary arterytime enhancement curve minus the injection duration of the test bolusplus an offset factor in recognition that the contrast arrives in theright atrium before it transits to the pulmonary trunk. A default valueof 2 seconds was used for the offset factor in several studies. As clearto those skilled in the art, the above considerations/logic apply toROIs other than the left heart/right heart.

The scan delay can, for example, be computed by estimating a bolusarrival time using the formula:scanDelay=T ₂−(T _(injTB)+arrOffset)+T _(start)wherein T_(injTB) is the injection duration of the timing bolus andarrOffset is an arrival time offset value; and a scan end time can bedetermined by adding the scan delay to the scan duration.

An arrival time of contrast in the right heart can, for example, becomputed using the formulaT _(arrRH) =T ₁−(T _(injTB)+arrOffset)wherein T_(1Peak) is the time to peak enhancement in the first region ofinterest.

FIG. 7A depicts a scenario in which the computed diagnostic injectionextends beyond the end of the scan. FIG. 7B depicts a resultingdiagnostic injection after a truncation algorithm or methodology of thepresent invention is executed. After the truncation, the injection isfinished a few seconds prior to the end of the scan (defined by thearrival time of the contrast to the right heart) ensuring that unneededcontrast is not injected into the patient. Because the protocolgeneration in this algorithm is data driven, it is not anticipated thatthe truncation operation described above will occur too frequently. Inthat regard, the duration of the injection is fitted via an optimizationmethodology using timing data generated from the test bolus. A morecommon scenario, however, is depicted in FIG. 8A. In this scenario, thecomputed diagnostic injection ends prior to the completion of the scan.However, the contrast injected in the last few seconds of the injectionwill not have enough time to migrate into the right heart (as determinedby the arrival time of contrast to the right heart measured from thepulmonary trunk time enhancement curve) and will not contribute to thediagnostic image. Therefore the injection is clamped/stopped at thedifference between the end of the scan and the arrival of contrast inthe right heart. The resulting injection protocol is presented in FIG.8B.

In that regard, the injection can be truncated if(T_(inj)+T_(arrRH))>scanEnd. The injection can, for example, betruncated so that it is finished at least T_(arrRH) seconds before endof the scan as follows:T _(inj)=scanEnd−T _(arrRH).

After the contrast injection protocol is checked and modified, ifnecessary, to prevent extension beyond the end of the scan and thatcontrast is not unnecessarily injected, a dual-flow (or dilution) phase,in which both contrast and a diluent are injected simultaneously, can becomputed. The approach of the present invention is different thanprevious embodiments in that every protocol does not necessarily have adual-flow protocol. The dilution phase is, for example, designed toreduce bright opacification of the superior vena cava (SVC) and rightheart structures, which may result in streak and beam hardeningartifacts.

In several embodiments, a comparison of the scan start and the injectionis made to determine when a dilution phase should be inserted. If thescan starts while the contrast injection is proceeding, it is reasonedthat diluted contrast should be “cut in”, or started, N seconds prior tothe start of the scan because the diluted contrast will be filling theright heart structures as the scan starts (where N is the arrival ofcontrast to the right heart). If the contrast dilution does not startwithin the time frame between the start of the scan minus the bolusarrival time into the right heart, than undiluted contrast will befilling the SVC etc., increasing the chance of streak and overopacification. A pictorial description of the dilution phase computationis provided in FIG. 9A. The resulting injection protocol with a DualFlowphase is given in FIG. 9B. As described above, the ratio ofcontrast/saline was fixed or dependent on scan/subject parameters to be40/60 (contrast/saline) in several studied to reduce the degrees offreedom in the experiment. As clear to one skilled in the art,contrast/saline ratios can readily be generated that are variable (forexample, as described in PCT International Patent Application No.PCT/US2007/026194 or as further described below). For example, a ratioof contrast enhancing fluid to non-contrast enhancing fluid in anadmixture or dual-flow phase can be determined on the basis of time topeak enhancement determined during the test bolus. A longer time to peakenhancement can, for example, result in a higher ratio of contrastenhancing fluid to non-contrast enhancing fluid.

The protocol generation algorithms described above can, for example, beused to minimize the dose of contrast a subject receives by consideringthat subject's cardiac dynamics, drug properties and scan properties.FIG. 10A sets forth flow rates calculated using the methodology of thepresent invention (B) as compared to the rates calculated using themethodology set forth in PCT International Patent Application No.PCT/US2007/026194 (A). The flow rates determined using the methodologyof the present invention are similar in magnitude to those calculatedusing the other methodology, yet show a greater variability, which onewould expect because the methodology of the present invention attemptsto generate more patient specific injection protocols with variable flowrates. The comparison is made as a check of the algorithms clinicalvalidity. For example, if a majority of resulting flow rate values werecalculated to be greater than 10 ml/s or less than 3 ml/s, this mightindicate a flaw in the algorithmic logic.

FIG. 10B illustrates data obtained in a study group of 70 patientsscheduled for clinically indicated dual source CT or DSCT studies usingmethodology 1 as described above. In the studies of the study group,contrast having a concentration of 300 mgI/ml was injected. A targetedattenuation level of 250 HU was used. ECG pulsing was also used tominimize radiation dosing. In the data, Asc.Aorta refers to AscendingAorta, Left_Main refers to the Coronary Artery, LAD_Proximal refers tothe Proximal Region of the Left Anterior Descending Coronary Artery,LAD_Middle refers to the Middle Region of the Left Anterior DescendingCoronary Artery, LAD_Distal refers to the Distal Region of the LeftAnterior Descending Coronary Artery, LCX_Proximal refers to the ProximalRegion of the Left Circumflex Artery, LCX_Middle refers to the MiddleRegion of the Left Circumflex Artery, LCX_Distal refers to the DistalRegion of the Left Circumflex Artery, RCA_Proximal refers to theProximal region of the Right Coronary Artery, RCA_Middle refers to theMiddle region of the Right Coronary Artery, and RCA_Distal refers to theDistal region of the RCA.

A control group of 50 patients scheduled for clinically indicated dualsource CT or DSCT studies was also studied. In the studies of thecontrol group, contrast having a concentration of 300 mgI/ml wasinjected. A routine triphasic injection protocol was used with thecontrol group. In the triphasic injection protocol, 60-90 ml of contrastmedium was first injected, followed by a dual flow injection of 50 ml offluid having a contrast medium/saline ration of 30/70, followed byinjection of saline. The flow rate for each phase was 6 ml/sec.

FIG. 10C illustrates mean attenuation (HU) for each of the anatomyregions studied for the study group. FIG. 10D illustrates mean contrastenhancement fluid or contrast medium volume used in the studies of eachof the study group and the control group. A mean savings ofapproximately 19.7±24.1 mL of contrast per patient was achieved usingthe methodology of the present invention. FIG. 10E illustrates a graphof contrast medium savings (mL) as a function of cardiac output. Asillustrated the systems and methods of the present invention providecontrast medium savings over a wide range of contrast medium. There arecases for subjects with high cardiac output that the algorithm computesa protocol that requires more contrast than would otherwise bedelivered. In those cases, it is possible that the standard controlprotocol would provide insufficient enhancement (<250 HU). FIG. 10Fillustrates mean attenuation for the control group and the study groupfor each of the regions studied. For the study group, there is lessvariability across regions (it is more consistently close to 250 HU) ascompared to the control, which has inconsistent enhancement patterns(note the higher enhancement in the Asc Aorta and the lower enhancementin the distal regions).

A summary of the workflow of the above-identified embodiment of amethodology of the present invention as applied in connection with thepulmonary artery and ascending aorta is set forth below:

-   -   1: Get Patient and Procedure information:        -   a. Get contrast concentration: C_(i)        -   b. Get the maximum flow rate allowable: Q_(MAX)        -   c. Get scan duration from user: ΔT        -   d. Get Hounsfield to plasma concentration conversion factor            HutoMgI for the scanner (default=25 HU/(mgI/ml))        -   e. Get desired peak enhancement DesiredPeak and desired            target enhancement at start and stop of scan window            DesiredTarget        -   f. Generate a test bolus injection protocol, default Q is 5            ml/s and volume=20 ml (4 second T_(inj)), saline flush            phase, Q=5 ml/s, vol=40 ml    -   2: From test bolus, get times to peak for the pulmonary artery        enhancement curve and the ascending aorta enhancement curve from        user: T₁ and T₂    -   3: Get peak enhancement values from the pulmonary artery and the        ascending aorta bolus enhancement curves, and convert to        concentration units using HutoMgI C_(1PA) and C_(2AO)    -   4: Estimate Cardiac Output and Blood Volume Subroutine        -   a. Compute Cardiac Output estimate (Q_(CO)) using Equation 7        -   b. Compute Blood Volume estimate (V_(B)) using Equation 6    -   5: Estimate Diagnostic Protocol Subroutine        -   a. Compute peak (C_(Peak)) and target (C_(Target))            enhancements in 1 the aorta using Equations (9) and (13),            respectively, for all admissible input values for T_(inj)            and Q_(inj)            -   i. Maximum Q_(inj)=maxFlowRate            -   ii. Minimum Q_(inj)=3.5 ml/s for 300 mgI/ml contrast,                2.8 ml/s for 370 mgI/ml contrast (Iodine administration                rate of 1 gI/s per Rist et al)            -   iii. Maximim T_(inj)=ΔT+8            -   iv. Minimum T_(inj)=ΔT        -   b. Find values for the diagnostic protocol flow rate            Q*_(inj) and injection duration T*_(inj) which are the            arguments that minimize the cost function in Equation 8:    -   6: Compute Injection Protocol Subroutine—Including Dilution        Phase        -   a. Compute the total diagnostic phase contrast volume:            Vol_(tot)=Q_(inj)*T_(inj)        -   b. Define an arrival time offset value: arrOffset=2 seconds        -   c. Compute the scan delay by estimating the bolus arrival            time, where T₂ is the time to the second peak:            scanDelay=T₂−(T_(injTB)+arrOffset)+T_(start)        -   d. Compute the end point of the scan: scanEnd=scanDelay+ΔT        -   e. Compute the arrival time of the contrast in the right            heart, where T₁ is the time to the first peak:            T_(arrRH)=T₁−(T_(injTB)+arrOffset)        -   f. Use the computed T_(arrRH), scanEnd, and T_(inj) to            determine if/when the injection should be truncated.            -   i. if (T_(inj)+T_(arrRH))>scanEnd            -   ii. then we truncate the injection protocol so that it                is finished at least TarrRH seconds before end of the                scan: T_(inj)=scanEnd−T_(arrRH)        -   g. Use the computed T_(arrRH), scanDelay, and T_(inj) to            determine if/when a dilution DualFlow phase should be            initiated.            -   i. if (T_(inj)+T_(arrRH))>scanDelay            -   ii. then we “cut over” to the DualFlow phase so that                diluted contrast is entering the right heart during the                scan: T_(startDF)=scanDelay−T_(arrRH)        -   h. Define DualFlow ratio: DF_(ratio)=0.40        -   i. Determine the duration of the DualFlow phase:            -   i. T_(endDF)=T_(inj)            -   ii. DF_(dur)=T_(endDF)−T_(startDF)        -   j. Compute volumes for three phases of injection:            -   i. Vol_(DF)=DF_(dur)*Q_(inj)            -   ii. Vol_(Contrast)=Vol_(tot)−Vol_(DF);            -   iii. Vol_(Saline)=40

In the above studies, an injection flow rate was calculated. It is alsopossible, for example, to vary the iodine administration rate during thediagnostic injection instead of the flow rate. The resulting enhancementgeometry may be slightly different. In one embodiment, the volumetricflow rate is fixed for all patient, but the Iodine Administration Rate(gI/s) is adjusted by diluting the contrast during the diagnosticinjection, if required. Only if the stock concentration cannot providesufficient enhancement, would the volumetric flow rate be increased.

In the embodiments described above, the scan begins at T_(start), on anunknown point on the upslope of the left heart concentration curve. Thescan ends ΔT seconds later (where ΔT is the specified scan duration) onthe downslope of the curve. To time the scan window in a manner toachieve relatively high and consistent enhancement, those two values(referred to as C_(LH-Start) on the upslope and C_(LH-End) on thedownslope) should be as close to C_(LH-Target) as possible. The rightheart curve has similar associated parameters. However, becauseC_(RH-Peak) should not occur during the scan window (as too muchenhancement in the right heart could lead to streaking or beam hardeningartifacts), it was not included as a term in the cost function set forthin Equation (8).

Diagnostic Injection Protocol Generation with Variable Dilution Ratioand Optimization for Concentration/Enhancement in an Additional Regionof Interest—Methodology 2

In another embodiment of a protocol generation system and method of thepresent invention, parameters are added in the optimization procedurerelated to the dilution phase. For example, the dilution ratio (R₂) andthe duration of the dilution phase (ΔT_(inj2)) can be added to theoptimization procedure. The dilution ratio is thereby personalized(instead of using a fixed or set ratio of, for example, 40/60). Further,there is no need to adjust the computed protocol after optimizationEnhancement targets are also added to the optimization procedure (forexample, cost function) for a second region of interest (the right heartor RH in the representative examples herein) in this embodiment. Becausethe best placement of the scan window does not depends solely on leftheart or LH enhancement in the representative examples of thisembodiment set forth herein, there is no analytic expression forT_(start). T_(start) is thus also included as a parameter in theoptimization procedure. FIG. 11 illustrates an example of relativetiming and diagnostic injection protocol phases, scan and enhancementcurves for the right heart/pulmonary artery and left heart/aorta.

Another term was added to cost function as a penalty on the total volumeof contrast injected (see the last term of the cost function of Equation(14)). Weighting factors such as α, β, and γ in Equation (14) wereincluded to allow for adjustment of the relative importance of the termsof the cost function. For example, by using a small value for α, errorin right heart enhancement is penalized less heavily than error in leftheart enhancement. Because the scan window is not centered on the rightheart peak, it is typical that C(T_(RH-Start)) or C_(RH-Start) will betoo high and C(T_(RH-End)) or C_(RH-End) will be too low. Therefore, toavoid having the optimization dominated by such errors in right heartenhancement, set α was set to equal 0.5 in several embodiments. β wasset to equal 1 in several embodiments, which was shown to be areasonable trade-off between losing consistency with the test bolus flowrate and not reaching target enhancement levels. In several embodimentsγ was set to equal 1000, which puts a very large penalty on exceedingthe loaded contrast volume. In that regard, if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) was true, γ was set to equal1000. Otherwise, γ was set to equal 0.

$\begin{matrix}{T_{start}^{\star},Q_{inj}^{\star},R_{1}^{\star},{\Delta T}_{{inj}1}^{\star}, R_{2}^{\star},{{\Delta\; T_{{inj}2}^{\star}} = {\underset{\underset{\underset{R_{2},{\Delta\; T_{{inj}\; 2}}}{R_{1},{\Delta\; T_{{inj}\; 1}},}}{T_{start},Q_{inj},}}{\arg\mspace{11mu}\min}\begin{pmatrix}{{{C_{{LH}\text{-}{Peak}} - C_{{LH}\text{-}{Peak}\text{-}{Desired}}}} +} \\{{{C_{{LH}\text{-}{Start}} - C_{{LH}\text{-}{Target}\text{-}{Desired}}}} +} \\{{{C_{{LH}\text{-}{End}} - C_{{LH}\text{-}{Target}\text{-}{Desired}}}} +} \\{{\alpha{{C_{{RH}\text{-}{Start}} - C_{{RH}\text{-}{Target}\text{-}{Desired}}}}} +} \\{{\alpha{{C_{{RH}\text{-}{End}} - C_{{RH}\text{-}{Target}\text{-}{Desired}}}}} +} \\{{\beta{{Q_{inj} - Q_{TB}}}} +} \\{\gamma,{{if}( {{Q_{inj}( {{R_{1}{\Delta T}_{{inj}\; 1}} + {R_{2}\Delta\; T_{{inj}\; 2}}} )} > V_{Load}} )}}\end{pmatrix}}}} & (14)\end{matrix}$Depending on the dilution ratios, the peak value for the LH occursduring the upslope (phase 1) or dilution phase (phase 2), and istherefore the greater of the two:

$\begin{matrix}{C_{{LH}\text{-}{Peak}} = {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 1}}} )}}} & (15) \\{{or}{C_{{LH}\text{-}{Peak}} = {{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 2}}} + {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 2}}} )}}}}} & (16)\end{matrix}$For the remaining concentration values, given an absolute time T (eitherthe start or end of the scan), the RH and LH curves can each be in oneof 3 regions—upslope (phase 1), dilution (phase 2), or decay (phase 3).When T<(T_(arr)+ΔT_(inj1)), the expression is:

$\begin{matrix}{C_{T} = {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - T_{arr}})}}} )}}} & (17)\end{matrix}$Note that T_(arr) is either T_(RH-arr) or T_(LH-arr), depending on whichcurve is being used. For the dilution phase (phase 2), when(T_(arr)+ΔT_(inj1))<T<(T_(arr)+ΔT_(inj1)+ΔT_(inj2)), the expression is:

$\begin{matrix}{C_{T} = {{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{arr} + {\Delta\; T_{{inj}\; 1}}})}})}}} + {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{arr} + {\Delta\; T_{{inj}\; 1}}})}})}}} )}}}} & (18)\end{matrix}$Finally, in the decay phase (phase 3), whenT>(T_(arr)+ΔT_(injA)+ΔT_(injAB)), the expression is:

$\begin{matrix}{C_{T} = {\begin{pmatrix}{{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 2}}} +} \\{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}2}}} )}}\end{pmatrix}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{arr} + {\Delta\; T_{{inj}\; 1}} + {\Delta\; T_{{inj}\; 2}}})}})}}}} & (19)\end{matrix}$

Therefore, to find a given concentration on a given curve at a giventime, one specifies the arrival time corresponding to the curve (RH orLH), determines which phase is occurring at time T, and uses theappropriate equation as set forth above.

Although the search space grew from a two-dimensional search space inEquation (8) to six-dimensional search space in Equation (14), a bruteforce search strategy was still implemented. The parameter range is welldefined, the solution manifold is well behaved and the computationalburden needed to search for the minimum is still not significant in thecase of a relatively coarsely sampled grid (for example, flow rates at0.1 ml/s, dilution ratios at 10%, and times at 1 second). Further, acomputation time of several seconds in the interval between parameterentry and protocol generation has no impact on the imaging procedure.

Similar to the previous embodiment, the protocol generation proceduredescribed above can be used to minimize the dose of contrast a subjectreceives considering the subject's cardiac dynamics, the drug propertiesand the scan properties. FIGS. 12 and 13, respectively, present iodineadministration rates and total contrast volumes using the optimizationprocedure of Equation (14) (C) as compared to the methodology set forthin PCT International Patent Application No. PCT/US2007/026194 (A), andthe methodology encompassing the optimization procedure of Equation (14)(B). The comparison provides a check of clinical validity.

FIG. 14 illustrates clinical data collected from ten subjects undergoingDSCT cardiac imaging (Siemens Definition) under methodology 2 asdescribed above. Mean values set forth in FIG. 14 are the mean of threeregions of interests placed in each of the anatomical regions. Thetarget enhancement for all anatomical regions (except for the pulmonaryartery trunk and the right ventricle) was 300 HU. The error barsillustrated are ±−1 standard deviation. The anatomical regions studiedwere Part (Pulmonary Artery Trunk), AscAorta (Ascending Aorta), RV(Right Ventricle), LftMain (Left Main Coronary Artery), LAD Prox(Proximal Region of the Left Anterior Descending Coronary Artery), LADDist (Distal region of the LAD coronary artery), RCA Prox (Proximalregion of the Right Coronary Artery), RCA Dist (Distal region of theRCA).

A summary of the workflow of the above-identified embodiment of amethodology of the present invention (methodology 2) as applied inconnection with the pulmonary artery and ascending aorta is set forthbelow:

-   -   1: Get Patient and Procedure information:        -   a. Get contrast concentration: C_(i)        -   b. Get the maximum flow rate allowable: Q_(MAX)        -   c. Get scan duration from user: ΔT        -   d. Get Hounsfield to plasma concentration conversion factor            HutoMgI for the scanner (default=25 HU/(mgI/ml))        -   e. Get desired LH enhancement at start and stop of scan            window LHTarget and desired RH enhancement at start and stop            of scan window RHTarget        -   f. Generate a test bolus injection protocol, default Q is 5            ml/s and volume=20 ml (4 second T_(inj)), at a 50/50            contrast ratio, followed by saline flush phase, Q=5 ml/s,            vol=40 ml    -   2: From test bolus, get times to peak for the pulmonary artery        enhancement curve and the ascending aorta enhancement curve from        user: T₁ and T₂    -   3: Get peak enhancement values from the pulmonary artery and the        ascending aorta bolus enhancement curves, and convert to        concentration units using HutoMgI: C_(1PA) and C_(2AO)    -   4: Estimate Cardiac Output and Blood Volume Subroutine        -   a. Compute Cardiac Output estimate (Q_(CO)) using Equation            (7).        -   b. Compute Blood Volume estimate (V_(B)) using Equation (6)    -   5: Estimate Diagnostic Protocol Subroutine        -   a. Compute peak C_(LH) _(—) _(Peak), C_(LH) _(—) _(start),            C_(LH) _(—) _(end), C_(RH) _(—) _(start), and C_(RH) _(—)            _(end) enhancements using Equations 9, 10, 11, 12 and 13,            respectively, for all admissible input values for T_(start),            Q_(inj), R₁, ΔT_(inj1), R₂, ΔT_(inj2).            -   i. T_(start) range=T_(LH-arr) to 30            -   ii. Q_(inj) range=Q_(injTB) to min(Q_(injTB)+1, Q_(MAX))            -   iii. R₁ range=0.1 to 1.0            -   iv. ΔT_(inj1) range=ΔT_(scan) to ΔT_(scan)+8            -   v. R₂ range=0.05 to 0.95            -   vi. ΔT_(inj2) range=0 to ΔT_(scan)        -   b. Find values for T*_(start), Q*_(inj1), R*₁, ΔT*_(inj1),            R*₂, ΔT*_(inj2), which are the arguments that minimize the            cost function of Equation 14.

The foregoing description and accompanying drawings set forth thepreferred embodiments of the invention at the present time. Variousmodifications, additions and alternative designs will, of course, becomeapparent to those skilled in the art in light of the foregoing teachingswithout departing from the scope of the invention. The scope of theinvention is indicated by the following claims rather than by theforegoing description. All changes and variations that fall within themeaning and range of equivalency of the claims are to be embraced withintheir scope.

What is claimed is:
 1. A method of determining at least one parameterfor an injection procedure to be performed in combination with animaging procedure, the method comprising the steps of: (a) injecting atest bolus of a contrast enhancement fluid having a contrast enhancingagent therein; (b) scanning at least two regions of interest with animaging system as the test bolus of the contrast enhancement fluid flowstherethrough to obtain therefrom a contrast time enhancement curve foreach of the at least two regions of interest; (c) extracting at leastone discrete data point from each of the contrast time enhancementcurves such that each of the discrete data points constitutes a pair ofmeasurements on the contrast time enhancement curve correspondingthereto; (d) substituting into a model the discrete data pointsextracted from the contrast time enhancement curves to obtain therefromat least an estimate of values of physiological variables; and (e) usingthe at least an estimate of the values of the physiological variables todetermine via the model the at least one parameter for the injectionprocedure to be performed in combination with the imaging procedure. 2.The method of claim 1 wherein the physiological variables are related tocardiopulmonary function.
 3. The method of claim 2 wherein the at leastone parameter is a parameter of at least one phase of the injectionprocedure for the injection of the contrast enhancement fluid or aparameter of the imaging system.
 4. The method of claim 2 wherein thediscrete data point(s) from the contrast time enhancement curve of afirst of the regions of interest corresponds to a first pass of thecontrast enhancement fluid through the first region of interest, and thediscrete data point(s) from the contrast time enhancement curve of asecond of the regions of interest corresponds to a first pass of thecontrast enhancement fluid through the second region of interest.
 5. Themethod of claim 4 wherein an analyzed portion of the contrast timeenhancement curve of the first region of interest overlaps an analyzedportion of the contrast time enhancement curve of the second region ofinterest in time.
 6. The method of claim 4 wherein a contrast enhancingagent concentration on one of the contrast time enhancement curves at acertain time is related to a contrast enhancing agent concentration onthe other of the contrast time enhancement curves at the certain time ora time in proximity to the certain time using a conservation of massbalance.
 7. The method of claim 6 wherein it is assumed that the loss ofthe contrast enhancement fluid between the first region of interest andthe second region of interest is negligible.
 8. The method of claim 7wherein it is assumed that the blood volume for the first region ofinterest is equal to the blood volume for the second region of interest.9. The method of claim 2 wherein the model is a physiological model inwhich cardiac output and blood volume are the physiological variables,the cardiac output and the blood volume between the injection site and ameasurement point of each of the regions of interest are calculated fora patient, and the at least one parameter is determined using thephysiological model.
 10. The method of claim 8 wherein the model is aphysiological model in which cardiac output and blood volume arephysiological variables, the cardiac output and the blood volume betweenthe injection site and a measurement point of each of the regions ofinterest are calculated for a patient, and the at least one parameter isdetermined using the physiological model.
 11. The method of claim 10wherein a time to peak enhancement for first region of interestenhancement T₁ and a time to peak enhancement for the second region ofinterest enhancement T₂ are input into the physiological model.
 12. Themethod of claim 11 wherein concentration at peak enhancement for thefirst region of interest enhancement C₁(T₁) and concentration at peakenhancement for the second region of interest enhancement C₂(T₂) areinput into the physiological model.
 13. The method of claim 12 wherein adistribution of contrast enhancement fluid in each region of interestwhich is injected from a peripheral injection site is described by thefollowing physiological model analytical solution:${C_{o}(t)} = \{ \begin{matrix}{{\frac{Q_{inj}}{Q_{CO}}{C_{i}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}t}} )}\mspace{14mu} t} \leq T_{inj}} \\{{{C_{o}( T_{inj} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({t - T_{inj}})}}t} > T_{inj}}\end{matrix} $ wherein the origin, t=0, corresponds to the timeat which contrast arrives in the region of interest, Q_(inj)[ml/s] isthe injection flow rate, T_(inj)[s] is the injection duration, Q_(CO) isthe cardiac output [ml/s], V_(B) is the blood volume [ml] between theinjection site and a measurement point of each of the regions ofinterest, C_(i) is the concentration of contrast in a contrast sourcefrom which contrast is injected into the patient, and C_(o)(t) is theblood concentration in the region of interest of the agent at time t.14. The method of claim 13 wherein concentration is related toenhancement level by the formula:C _(O)(t)=s(t)/K wherein s(t) [Hounsfield units or HU] is enhancementlevel at time t and K [mgI/ml] is a conversion factor.
 15. The method ofclaim 14 wherein T_(inj) is the injection duration and is amount of timebetween arrival of the contrast enhancement agent and the time to peakenhancement.
 16. The method of claim 15 wherein:${C_{o}( T_{inj} )} = {\frac{\max\;{s_{2}( T_{2} )}}{K} = {C_{2}( T_{2} )}}$wherein max s₂(T₂) [Hu] is the maximum enhancement level in the secondregion of interest and C₂(T₂) is the concentration at peak enhancementfor the second region of interest enhancement.
 17. The method of claim14 wherein concentration in the first region of interest C₁ at time T₂is estimated by the following formula:C ₁(T ₂)≈C ₁(T ₁)C ₂(T ₂) wherein C₁(T₁) is the concentration in thefirst region of interest C₁ at time T₁ and C₂(T₂) is the concentrationin the second region of interest C₂ at time T₂.
 18. The method of claim17 wherein blood volume V_(B) is determined using one of the followingformulas:$V_{B} = {{\frac{{- T_{1}}Q_{CO}}{\log\lbrack {1 - {\frac{C_{1}( T_{1} )}{Q_{inj}C_{i}}Q_{CO}}} \rbrack}\mspace{14mu} V_{B}} = {\frac{{- ( {T_{2}T_{1}} )}Q_{CO}}{\log\lbrack \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} \rbrack}.}}$19. The method of claim 18 wherein cardiac output Q_(CO) is determinedusing the following formula:$Q_{CO} = {\frac{Q_{inj}}{C( T_{1} )}{{C_{i}\lbrack {1 - ( \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} )} \rbrack}^{\frac{T_{1}}{T_{2} - T_{1}}}.}}$20. The method of claim 19 wherein the determined value of Q_(CO) isused in the physiological model to determine the at least one parameter.21. The of claim 20 wherein concentration of contrast agent at peakenhancement C(T_(Peak)) at the time of peak enhancement T_(Peak) in thesecond region of interest of an imaging injection is related to theinjection flow rate Q_(inj) of the imaging injection and the injectionduration T_(inj) of the imaging injection using the formula:${C( T_{Peak} )} = {\frac{Q_{inj}}{Q_{CO}}{{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}.}}$22. The method of claim 21 wherein a concentration of contrast agent inthe second region of interest at time of a scan start, C(T_(start)), isprovided by:${C( T_{start} )} = \frac{\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}{1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}} + {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T_{inj} - {\Delta\; T}})}}}$wherein ΔT is the scan duration and wherein C(T_(start)) is equal toC(T_(start)+ΔT).
 23. The method of claim 22 wherein C(T_(Peak)) andC(T_(start)) enhancements are determined for admissible input values forT_(inj) and Q_(inj) wherein a maximum Q_(inj) and a minimum Q_(inj) anda maximum T_(inj) and a minimum T_(inj) are established.
 24. The methodof claim 23 wherein maximum T_(inj) is established as a function of scanduration plus a constant, minimum T_(inj) is established as the scanduration.
 25. The method of claim 24 wherein values for a diagnosticprotocol flow rate Q*_(imj) and an injection duration T*_(inj) aredetermined which are the arguments that minimize the cost function:$Q_{inj}^{\star},{T_{inj}^{\star} = {\underset{Q_{inj},T_{inj}}{\arg\;\min_{\;}}{( {{{{DesiredPeak} - {C( T_{Peak} )}}} + {{{DesiredTarget} - {C( T_{start} )}}}} ).}}}$26. The method of claim 20 wherein the first region of interest is thepulmonary artery and the second region of interest is the ascendingaorta and values for a diagnostic protocol flow rate are determinedwhich are the arguments that minimize the cost function:$T_{start}^{\star},Q_{inj}^{\star},R_{1}^{\star},{\Delta\; T_{{inj}\; 1}^{\star}},R_{2}^{\star},{{\Delta\; T_{{inj}\; 2}^{\star}} = {\underset{\underset{\underset{R_{2},{\Delta\; T_{{inj}\; 2}}}{R_{1},{\Delta\; T_{{inj}\; 1}}},}{T_{start},Q_{inj},}}{\arg\;\min}\begin{pmatrix}{{{C_{{LH}\text{-}{Peak}} - C_{{LH}\text{-}{Peak}\text{-}{Desired}}}} +} \\{{{C_{{LH}\text{-}{Start}} - C_{{LH}\text{-}{Target}\text{-}{Desired}}}} +} \\{{{C_{{LH}\text{-}{End}} - C_{{LH}\text{-}{Target}\text{-}{Desired}}}} +} \\{{\alpha{{C_{{RH}\text{-}{Start}} - C_{{RH}\text{-}{Target}\text{-}{Desired}}}}} +} \\{{\alpha{{C_{{RH}\text{-}{End}} - C_{{RH}\text{-}{Target}\text{-}{Desired}}}}} +} \\{{\beta{{Q_{inj} - Q_{TB}}}} +} \\{\gamma,{{if}( {{Q_{inj}( {{R_{1}\Delta\; T_{{inj}1}} + {R_{2}\Delta\; T_{{inj}2}}} )} > V_{Load}} )}}\end{pmatrix}}}$ wherein T_(start) is a time of start of a scan, R₁ is arate of injection in a phase wherein only contrast medium is injected,ΔT_(inj1) is the time of duration of the phase wherein only contrastmedium is injected, R₂ is a rate of injection in a phase whereincontrast medium and diluent are injected, ΔT_(inj2) is the time ofduration of the phase wherein contrast medium and diluent are injected,C_(LH-Peak) is a calculated concentration at peak enhancement in theleft heart, C_(LH-Desired) is a desired concentration at peakenhancement in the left heart, C_(LH-Start) is a calculatedconcentration in the left heart at the time of start of the scan,C_(LH-Target-Desired) is a desired concentration in the left heart atthe time of start of the scan, C_(LH-End) is a calculated concentrationin the left heart at the time of the end of the scan or T_(End),C_(RH-Start) is a calculated concentration in the right heart at thetime of start of the scan, C_(RH-Target-Desired) is a desiredconcentration in the right heart at the time of start of the scan, andC_(RH-End) is a calculated concentration in the right heart at the timeof the end of the scan, α is a weighting factor, β is a weighting factorand γ is a penalty value, wherein γ is not zero if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) is true and is zero if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(load)) is not true, whereinV_(Load) is the total volume of contrast available.
 27. The method ofclaim 26 wherein C_(LH-Peak) is the greater of the value calculated asfollows:$\mspace{79mu}{C_{{LH}\text{-}{Peak}} = {\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 1}}} )}\mspace{14mu}{or}}}$$C_{{LH}\text{-}{Peak}} = {{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 2}}} + {\frac{Q_{inj}}{Q_{CO}}C_{i}{{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 2}}} )}.}}}$28. The method of claim 27 wherein concentration C_(T) in the rightheart or the left heart as applicable at a time T, which is eitherT_(start) or T_(end), when T<(T_(arr)+ΔT_(inj1)), wherein T_(arr) iseither the time of arrival of contrast at the right heart or at the leftheart as applicable, is calculated by the following formula:$C_{T} = {\frac{Q_{inj}}{Q_{CO}}C_{i}{{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - T_{arr}})}}} )}.}}$29. The method of claim 27 wherein concentration C_(T) in the rightheart or the left heart as applicable at a time T, when(T_(arr)+ΔT_(inj1))<T<(T_(arr)+ΔT_(inj1)+ΔT_(inj2)), is calculated bythe following formula:$C_{T} = {{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{arr} + {\Delta\; T_{{inj}\; 1}}})}})}}} + {\frac{Q_{inj}}{Q_{CO}}C_{i}{{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{arr} + {\Delta\; T_{{inj}\; 1}}})}})}}} )}.}}}$30. The method of claim 27 wherein concentration C_(T) in the rightheart or the left heart as applicable at a time T, when,T>(T_(arr)+ΔT_(injA)+ΔT_(injAB)) is calculated by the following formula:$C_{T} = {\begin{pmatrix}{{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{1}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}1}}} )}{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}\Delta\; T_{{inj}\; 2}}} +} \\{\frac{Q_{inj}}{Q_{CO}}C_{i}{R_{2}( {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{\Delta T}_{{inj}2}}} )}}\end{pmatrix}{\quad{{\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}{({T - {({T_{arr} + {\Delta\; T_{{inj}\; 1}} + {\Delta\; T_{{inj}\; 2}}})}})}}.}}}$31. The method of claim 2 wherein the first region of interest is thepulmonary artery and the second region of interest is the ascendingaorta.
 32. The method of claim 2 wherein the physiological variables areused in connection with the model or at least one other model todetermine the at least one parameter.
 33. The method of claim 32 whereinthe at least one other model is a parametric model.
 34. The method ofclaim 1 wherein the steps (d) and (e) include: (I) one of two equationsfor blood volume, V_(B): $\begin{matrix}{V_{B} = \frac{{- T_{1}}Q_{CO}}{\log\lbrack {1 - {\frac{C_{1}( T_{1} )}{Q_{inj}C_{i}}Q_{CO}}} \rbrack}} & {V_{B} = \frac{{- ( {T_{2} - T_{1}} )}Q_{CO}}{\log\lbrack \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} \rbrack}}\end{matrix}$ and an equation for cardiac output, Q_(CO):$Q_{CO} = {\frac{Q_{inj}}{C( T_{1} )}{C_{i}\lbrack {1 - ( \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} )} \rbrack}^{\frac{T_{1}}{T_{2} - T_{1}}}}$into which at least the pair of measurements of each of the discretedata points are input to solve for the blood volume, V_(B), and thecardiac output, Q_(CO); and (II) an automated iterative processinvolving use of at least the following equations:${{C( T_{Peak} )} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}}\mspace{14mu}$and${C( T_{start} )} = \frac{\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}{1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}} + e^{\frac{- Q_{CO}}{V_{B}}{({T_{inj} - {\Delta\; T}})}}}$into which the blood volume, V_(B), and the cardiac output, Q_(CO), areinput and into which maximum through minimum values for each of at leastan injection flow rate, Q_(inj), and an injection duration, T_(inj), areinput iteratively to ascertain values for C(T_(Peak)) and C(T_(start))that minimize the cost function:$Q_{inj}^{*},{T_{inj}^{*} = {\underset{Q_{inj},T_{inj}}{\arg\mspace{14mu}\min}( {{{{DesiredPeak} - {C( T_{Peak} )}}} + {{{DesiredTarget} - {C( T_{start} )}}}} )}}$such that the values for the injection flow rate, Q_(inj), and theinjection duration, T_(inj), that minimize the cost function are two ofthe at least one parameter of the injection procedure to be performed,wherein C(T_(Peak)) is a concentration of the contrast enhancing agentat peak enhancement and C(T_(start)) is a concentration of the contrastenhancing agent at a time of a start of the scanning by the imagingsystem, and the values of desired peak concentration, DesiredPeak, anddesired target concentration, DesiredTarget, of the contrast enhancingagent in at least one of the at least two regions of interest areoperator-entered into the cost function.
 35. The method of claim 1wherein the steps (d) and (e) include: (I) one of two equations forblood volume, V_(B):$V_{B} = {{\frac{{- T_{1}}Q_{CO}}{\log\lbrack {1 - {\frac{C_{1}( T_{1} )}{Q_{inj}C_{i}}Q_{CO}}} \rbrack}\mspace{14mu} V_{B}} = \frac{{- ( {T_{2} - T_{1}} )}Q_{CO}}{\log\lbrack \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} \rbrack}}$and an equation for cardiac output, Q_(CO):$Q_{CO} = {\frac{Q_{inj}}{C( T_{1} )}{C_{i}\lbrack {1 - ( \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} )} \rbrack}^{\frac{T_{1}}{T_{2} - T_{1}}}}$into which at least the pair of measurements of each of the discretedata points are input to solve for the blood volume, V_(B), and thecardiac output, Q_(CO); and (II) an automated iterative processinvolving use of at least the following equations:${{C( T_{Peak} )} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}}\mspace{14mu}$and${C( T_{start} )} = \frac{\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}{1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}} + e^{\frac{- Q_{CO}}{V_{B}}{({T_{inj} - {\Delta\; T}})}}}$into which the blood volume, V_(B), and the cardiac output, Q_(CO), areinput and into which maximum through minimum values for each of at leastan injection flow rate, Q_(inj), and an injection duration, T_(inj), areinput iteratively to ascertain values for C(T_(Peak)) and C(T_(start))that minimize the cost function:$T_{start}^{*},Q_{inj}^{*},R_{1}^{*},{\Delta\; T_{{inj}\; 1}^{*}},R_{2}^{*},{{\Delta\; T_{{inj}\; 2}^{*}} = {\underset{R_{2},{\Delta\; T_{{inj}\; 2}}}{\underset{R_{1},{\Delta\; T_{{inj}\; 1}},}{\underset{T_{start},Q_{inj},}{\arg\mspace{14mu}\min}}}\begin{pmatrix}{{{C_{{LH} - {Peak}} - C_{{LH} - {Peak} - {Desired}}}} +} \\{{{C_{{LH} - {Start}} - C_{{LH} - {Target} - {Desired}}}} +} \\{{{C_{{LH} - {End}} - C_{{LH} - {Target} - {Desired}}}} +} \\{{\alpha{{C_{{RH} - {Start}} - C_{{RH} - {Target} - {Desired}}}}} +} \\{{\alpha{{C_{{RH} - {End}} - C_{{RH} - {Target} - {Desired}}}}} +} \\{{\beta{{Q_{inj} - Q_{TB}}}} +} \\{\gamma,{{if}\mspace{14mu}( {{Q_{inj}( {{R_{1}\Delta\; T_{{inj}\; 1}} + {R_{2}\Delta\; T_{{inj}\; 2}}} )} > V_{Load}} )}}\end{pmatrix}}}$ such that the values for the injection flow rate,Q_(inj), and the injection duration, T_(inj), that minimize the costfunction are two of the at least one parameter of the procedure to beperformed, wherein C(T_(Peak)) is a concentration of the contrastenhancing agent at peak enhancement and C(T_(start)) is a concentrationof the contrast enhancing agent at a time of a start of the scanning bythe imaging system, and wherein T_(start) is a time of start of a scan,R₁ is a rate of injection in a phase wherein only contrast medium isinjected, ΔT_(inj1) is the time of duration of the phase wherein onlycontrast medium is injected, R₂ is a rate of injection in a phasewherein contrast medium and diluent are injected, ΔT_(inj2) is the timeof duration of the phase wherein contrast medium and diluent areinjected, C_(LH-Peak) is a calculated concentration at peak enhancementin the left heart, C_(LH-Desired) is a desired concentration at peakenhancement in the left heart, C_(LH-Start) is a calculatedconcentration in the left heart at the time of start of the scan,C_(LH-Target-Desired) is a desired concentration in the left heart atthe time of start of the scan, C_(LH-End) is a calculated concentrationin the left heart at the time of the end of the scan or T_(End),C_(RH-Start) is a calculated concentration in the right heart at thetime of start of the scan, C_(RH-Target-Desired) is a desiredconcentration in the right heart at the time of start of the scan, andC_(RH-End) is a calculated concentration in the right heart at the timeof the end of the scan, α is a weighting factor, β is a weighting factorand γ is a penalty value, wherein γ is not zero if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) is true and is zero if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) is not true, whereinV_(Load) is the total volume of contrast available, and the values ofdesired peak concentration, DesiredPeak, and desired targetconcentration, DesiredTarget, of the contrast enhancing agent in atleast one of the at least two regions of interest are operator-enteredinto the cost function.
 36. A method of determining at least oneparameter for a procedure, the method comprising the steps of: (a)injecting a test bolus of a pharmaceutical; (b) measuring at least tworegions of interest with a sensor as the test bolus of thepharmaceutical flows therethrough to obtain therefrom a timeconcentration curve for each of the at least two regions of interest;(c) extracting at least one discrete data point from each of the timeconcentration curves such that each of the discrete data pointsconstitutes a pair of measurements on the time concentration curvecorresponding thereto; and (d) determining the at least one parameterfor the procedure to be performed by substituting into a model thediscrete data points extracted from the time concentration curves. 37.The method of claim 36 wherein a sufficient number of the discrete datapoints are substituted into the model to determine values forphysiological variables in the model, the variables being related tocardiopulmonary function and for use in determining the at least oneparameter for the procedure to be performed.
 38. The method of claim 36wherein the step of substituting the discrete data points into the modelfor use in determining the at least one parameter for the procedureincludes: (a) one of two equations for blood volume, V_(B):$V_{B} = {{\frac{{- T_{1}}Q_{CO}}{\log\lbrack {1 - {\frac{C_{1}( T_{1} )}{Q_{inj}C_{i}}Q_{CO}}} \rbrack}\mspace{14mu} V_{B}} = \frac{{- ( {T_{2} - T_{1}} )}Q_{CO}}{\log\lbrack \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} \rbrack}}$and an equation for cardiac output, Q_(CO):$Q_{CO} = {\frac{Q_{inj}}{C( T_{1} )}{C_{i}\lbrack {1 - ( \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} )} \rbrack}^{\frac{T_{1}}{T_{2} - T_{1}}}}$into which at least the pair of measurements of each of the discretedata points are input to solve for the blood volume, V_(B), and thecardiac output, Q_(CO); and (b) an automated iterative process involvinguse of at least the following equations:${{C( T_{Peak} )} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}}\mspace{14mu}$and${C( T_{start} )} = \frac{\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}{1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}} + e^{\frac{- Q_{CO}}{V_{B}}{({T_{inj} - {\Delta\; T}})}}}$into which the blood volume, V_(B), and the cardiac output, Q_(CO), areinput and into which maximum through minimum values for each of at leastan injection flow rate, Q_(inj), and an injection duration, T_(inj), areinput iteratively to ascertain values for C(T_(Peak)) and C(T_(start))that minimize the cost function:$Q_{inj}^{*},{T_{inj}^{*} = {\underset{Q_{inj},T_{inj}}{\arg\mspace{14mu}\min}( {{{{DesiredPeak} - {C( T_{Peak} )}}} + {{{DesiredTarget} - {C( T_{start} )}}}} )}}$such that the values for the injection flow rate, Q_(inj), and theinjection duration, T_(inj), that minimize the cost function are two ofthe at least one parameter of the procedure, wherein C(T_(Peak)) is aconcentration of the pharmaceutical at peak enhancement and C(T_(start))is a concentration of the pharmaceutical at a time of a start of themeasurement by the sensor, and the values of desired peak concentration,DesiredPeak, and desired target concentration, DesiredTarget, of thepharmaceutical in at least one of the at least two regions of interestare operator-entered into the cost function.
 39. The method of claim 36wherein the step of substituting the discrete data points into the modelfor use in determining the at least one parameter for the procedureincludes: (a) one of two equations for blood volume, V_(B):$V_{B} = {{\frac{{- T_{1}}Q_{CO}}{\log\lbrack {1 - {\frac{C_{1}( T_{1} )}{Q_{inj}C_{i}}Q_{CO}}} \rbrack}\mspace{14mu} V_{B}} = \frac{{- ( {T_{2} - T_{1}} )}Q_{CO}}{\log\lbrack \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} \rbrack}}$and an equation for cardiac output, Q_(CO):$Q_{CO} = {\frac{Q_{inj}}{C( T_{1} )}{C_{i}\lbrack {1 - ( \frac{{C_{1}( T_{1} )} - {C_{2}( T_{2} )}}{C_{1}( T_{1} )} )} \rbrack}^{\frac{T_{1}}{T_{2} - T_{1}}}}$into which at least the pair of measurements of each of the discretedata points are input to solve for the blood volume, V_(B), and thecardiac output, Q_(CO); and (b) an automated iterative process involvinguse of at least the following equations:${{C( T_{Peak} )} = {\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}}\mspace{14mu}$and${C( T_{start} )} = \frac{\frac{Q_{inj}}{Q_{CO}}{C_{i}\lbrack {1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}}} \rbrack}}{1 - {\mathbb{e}}^{\frac{- Q_{CO}}{V_{B}}T_{inj}} + e^{\frac{- Q_{CO}}{V_{B}}{({T_{inj} - {\Delta\; T}})}}}$into which the blood volume, V_(B), and the cardiac output, Q_(CO), areinput and into which maximum through minimum values for each of at leastan injection flow rate, Q_(inj), and an injection duration, T_(inj), areinput iteratively to ascertain values for C(T_(Peak)) and C(T_(start))that minimize the cost function:$T_{start}^{*},Q_{inj}^{*},R_{1}^{*},{\Delta\; T_{{inj}\; 1}^{*}},R_{2}^{*},{{\Delta\; T_{{inj}\; 2}^{*}} = {\underset{R_{2},{\Delta\; T_{{inj}\; 2}}}{\underset{R_{1},{\Delta\; T_{{inj}\; 1}},}{\underset{T_{start},Q_{inj},}{\arg\mspace{14mu}\min}}}\begin{pmatrix}{{{C_{{LH} - {Peak}} - C_{{LH} - {Peak} - {Desired}}}} +} \\{{{C_{{LH} - {Start}} - C_{{LH} - {Target} - {Desired}}}} +} \\{{{C_{{LH} - {End}} - C_{{LH} - {Target} - {Desired}}}} +} \\{{\alpha{{C_{{RH} - {Start}} - C_{{RH} - {Target} - {Desired}}}}} +} \\{{\alpha{{C_{{RH} - {End}} - C_{{RH} - {Target} - {Desired}}}}} +} \\{{\beta{{Q_{inj} - Q_{TB}}}} +} \\{\gamma,{{if}\mspace{14mu}( {{Q_{inj}( {{R_{1}\Delta\; T_{{inj}\; 1}} + {R_{2}\Delta\; T_{{inj}\; 2}}} )} > V_{Load}} )}}\end{pmatrix}}}$ such that the values for the injection flow rate,Q_(inj), and the injection duration, T_(inj), that minimize the costfunction are two of the at least one parameter of the procedure, whereinC(T_(Peak)) is a concentration of the pharmaceutical at peak enhancementand C(T_(start)) is a concentration of the pharmaceutical at a time of astart of the measurement by the sensor, and wherein T_(start) is a timeof start of the measurement, R₁ is a rate of injection in a phasewherein only the pharmaceutical is injected, ΔT_(inj1) is the time ofduration of the phase wherein only the pharmaceutical is injected, R₂ isa rate of injection in a phase wherein the pharmaceutical and diluentare injected, ΔT_(inj2) is the time of duration of the phase wherein thepharmaceutical and diluent are injected, C_(LH-Peak) is a calculatedconcentration at peak enhancement in the left heart, C_(LH-Desired) is adesired concentration at peak enhancement in the left heart,C_(LH-Start) is a calculated concentration in the left heart at the timeof start of the measurement, C_(LH-Target-Desired) is a desiredconcentration in the left heart at the time of start of the measurement,C_(LH-End) is a calculated concentration in the left heart at the timeof the end of the measurement or T_(End), C_(RH-Start) is a calculatedconcentration in the right heart at the time of start of themeasurement, C_(RH-Target-Desired) is a desired concentration in theright heart at the time of start of the measurement, and C_(RH-End) is acalculated concentration in the right heart at the time of the end ofthe measurement, α is a weighting factor, β is a weighting factor and γis a penalty value, wherein γ is not zero if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) is true and is zero if(Q_(inj)(R₁ΔT_(inj1)+R₂ΔT_(inj2))>V_(Load)) is not true, whereinV_(Load) is the total volume of the pharmaceutical available, and thevalues of desired peak concentration, DesiredPeak, and desired targetconcentration, DesiredTarget, of the pharmaceutical in at least one ofthe at least two regions of interest are operator-entered into the costfunction.